Name Date Per. Ms. Williams/Mrs. Hertel
|
|
- Roxanne Fletcher
- 5 years ago
- Views:
Transcription
1 Name Date Per. Ms. Williams/Mrs. Hertel Day 7: Solving Exponential Word Problems involving Logarithms Warm Up Exponential growth occurs when a quantity increases by the same rate r in each period t. When this happens, the value of the quantity at any given time can be calculated as a function of the rate and the original amount. Exponential decay occurs when a quantity decreases by the same rate r in each time period t. Just like exponential growth, the value of the quantity at any given time can be calculated by using the rate and the original amount. In Summary,
2 Example 1: Growth The original value of a painting is $9,000 and the value increases by 7% each year. Part a: Then find the painting s value in 15 years. Part b: In what year, will the painting be worth $50,000? Example 2: Decay The population of a town is decreasing at a rate of 3% per year. In 2000 there were 1700 people. Part a: Find the population in Part b: In what year, will the population be double?
3 3) Is the equation A = 3200 (0.70) t a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period? Explain here! 1) exponential growth and 30% 2) exponential growth and 70% 3) exponential decay and 30% 4) exponential decay and 70% 4) Is the equation A = 1756 (1.17) t a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period? 1) exponential growth and 17% Explain here! 2) exponential growth and 83% 3) exponential decay and 17% 4) exponential decay and 83% 5)
4 Graphs of Logarithmic Functions Using the table below: a) Complete the table of values for y= 2 x b) sketch the graph of y= 2 x x y ) Recall: How do we find the inverse of a function? Properties of Domain: Properties of Domain: Range: Range: Find the inverse algebraically. Asymptote: Asymptote: x-intercept: x-intercept: y-intercept: y-intercept: 3) Graph the inverse of the function y = 2 x.
5 Rule for Graphing Exponential Functions Rule for Graphing Log Functions x y x y -1 1 b 1 b b 1 0 b 1
6
7
8 5. 6.
9 Exit Ticket
10 Word Problems Homework Day 1 Write an exponential growth/ decay function to model each situation. Then find the value of the function after the given number of years. 1) 2) 3) 4) Is the equation A = 10,000 (0.45) t a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period? 1) exponential growth and 45% 2) exponential growth and 55% Explain here! 3) exponential decay and 45% 4) exponential decay and 55% 5) Is the equation A = 5400 (1.07) t a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period? 1) exponential growth and 7% 2) exponential growth and 93% Explain here! 3) exponential decay and 7% 4) exponential decay and 93%
11 6) 7) Sketch below the graph of. Then, state the domain and range of the graph. Write the equation of the asymptote. 8)
12 Name Date Per. Ms. Williams/Mrs. Hertel Day 8: Solving Exponential Word Problems involving Logarithms Warm Up 1) In January 1995, the population of a small town was 8,000 people. Each year after 1995, the population decreased by 1%. a. Find the population of the town in January b. If this rate of decrease continues unchanged, what is the expected population of the town in January 2010? 2)
13 Example 1: Level A
14 Example 2: Level B
15 Example 3: Level A Example 4: Level B
16 Regents Question & Exit Ticket
17 Summary Exit Ticket
18 Day 8 Homework 1) 2) 3)
19 4) 5) 6)
20 7) 8) 9)
21 NAME: Algebra 2/Trig Unit 10: Logarithms REVIEW SHEET DATE: PERIOD: Converting and Solving Logarithms 1. Solve for x: log 3 (x - 1) = 2 5. Solve for x to the nearest hundredth: 2. Find the value of to four decimal places. Using the Power Law 6. Solve for x to the nearest thousandth: 3. The relationship between the relative size of an earthquake, S, and the measure of the earthquake on the Richter scale, R, is given by the equation log S = R. If an earthquake measured 6.2 on the Richter scale, what was its relative size to the nearest tenth? 7. Using logarithms, find w to the nearest tenthousandth: 4. The expression is equivalent to 1) 8 2) 2 3) 4)
22 Product and Quotient Laws 8. The expression is equivalent to 1) 3) 2) 4) Substitution with Logarithms 10. If and, what is? (1) x 2 y (3) x y 2 (2) 2x 2y y (4) x 2 9. The expression ( 1) 2) 3) 4) ) is equivalent to 11. Given: and Express in terms of p and q: Solving Logarithmic Equations 12. Solve algebraically for all values of x:
23 13. Solve for x: Undefined Logarithms 14. The expression log (x 2-4) is defined for all values of x such that (1) -2 x 2 (3) x 2 or x -2 (2) -2 < x < 2 (4) x > 2 or x < -2 Solving Logarithmic Word Problems 15. The scientists in a laboratory company raise amebas to sell to schools for use in biology classes. They know that one ameba divides into two amebas every hour and that the formula t = log 3 N can be used to determine how long in hours, t, it takes to produce a certain number of amebas, N. Determine, to the nearest hundredth of an hour, how long it takes to produce 5,000 amebas if they start with one ameba.
24 16. Sean invests $10,000 at an annual rate of 5% compounded continuously, according to the formula A Pe rt, where A is the amount, P is the principal, r is the rate of interest, and t is time, in years. Determine, to the nearest dollar, the amount of money he will have after 2 years. Determine how many years, to the nearest year, it will take for his initial investment to double. Inverse and Graphs of Logarithms 17. What is the inverse of the function y = log 3 x (1) 3 y = x (3) x 3 = y (2) 3 x = y (4) y = x Graph the equations on the same set of axes. State the domain and range of. Write the equation of the asymptote of.
Intermediate Algebra Chapter 12 Review
Intermediate Algebra Chapter 1 Review Set up a Table of Coordinates and graph the given functions. Find the y-intercept. Label at least three points on the graph. Your graph must have the correct shape.
More informationHW#1. Unit 4B Logarithmic Functions HW #1. 1) Which of the following is equivalent to y=log7 x? (1) y =x 7 (3) x = 7 y (2) x =y 7 (4) y =x 1/7
HW#1 Name Unit 4B Logarithmic Functions HW #1 Algebra II Mrs. Dailey 1) Which of the following is equivalent to y=log7 x? (1) y =x 7 (3) x = 7 y (2) x =y 7 (4) y =x 1/7 2) If the graph of y =6 x is reflected
More informationLogarithms involve the study of exponents so is it vital to know all the exponent laws.
Pre-Calculus Mathematics 12 4.1 Exponents Part 1 Goal: 1. Simplify and solve exponential expressions and equations Logarithms involve the study of exponents so is it vital to know all the exponent laws.
More informationAn equation of the form y = ab x where a 0 and the base b is a positive. x-axis (equation: y = 0) set of all real numbers
Algebra 2 Notes Section 7.1: Graph Exponential Growth Functions Objective(s): To graph and use exponential growth functions. Vocabulary: I. Exponential Function: An equation of the form y = ab x where
More informationObjectives. Use the number e to write and graph exponential functions representing realworld
Objectives Use the number e to write and graph exponential functions representing realworld situations. Solve equations and problems involving e or natural logarithms. natural logarithm Vocabulary natural
More informationAlgebra 2 - Classwork April 25, Review
Name: ID: A Algebra 2 - Classwork April 25, 204 - Review Graph the exponential function.. y 4 x 2. Find the annual percent increase or decrease that y 0.5(2.) x models. a. 20% increase c. 5% decrease b.
More informationExponential and Logarithmic Functions
Exponential and Logarithmic Functions Learning Targets 1. I can evaluate, analyze, and graph exponential functions. 2. I can solve problems involving exponential growth & decay. 3. I can evaluate expressions
More informationHonors Advanced Algebra Chapter 8 Exponential and Logarithmic Functions and Relations Target Goals
Honors Advanced Algebra Chapter 8 Exponential and Logarithmic Functions and Relations Target Goals By the end of this chapter, you should be able to Graph exponential growth functions. (8.1) Graph exponential
More informationChapter 11 Logarithms
Chapter 11 Logarithms Lesson 1: Introduction to Logs Lesson 2: Graphs of Logs Lesson 3: The Natural Log Lesson 4: Log Laws Lesson 5: Equations of Logs using Log Laws Lesson 6: Exponential Equations using
More informationPractice 6-1: Exponential Equations
Name Class Date Practice 6-1: Exponential Equations Which of the following are exponential functions? For those that are exponential functions, state the initial value and the base. For those that are
More informationExponential and Logarithmic Functions. 3. Pg #17-57 column; column and (need graph paper)
Algebra 2/Trig Unit 6 Notes Packet Name: Period: # Exponential and Logarithmic Functions 1. Worksheet 2. Worksheet 3. Pg 483-484 #17-57 column; 61-73 column and 76-77 (need graph paper) 4. Pg 483-484 #20-60
More informationEvaluate the exponential function at the specified value of x. 1) y = 4x, x = 3. 2) y = 2x, x = -3. 3) y = 243x, x = ) y = 16x, x = -0.
MAT 205-01C TEST 4 REVIEW (CHAP 13) NAME Evaluate the exponential function at the specified value of x. 1) y = 4x, x = 3 2) y = 2x, x = -3 3) y = 243x, x = 0.2 4) y = 16x, x = -0.25 Solve. 5) The number
More information4.6 (Part A) Exponential and Logarithmic Equations
4.6 (Part A) Eponential and Logarithmic Equations In this section you will learn to: solve eponential equations using like ases solve eponential equations using logarithms solve logarithmic equations using
More informationSection 4.2 Logarithmic Functions & Applications
34 Section 4.2 Logarithmic Functions & Applications Recall that exponential functions are one-to-one since every horizontal line passes through at most one point on the graph of y = b x. So, an exponential
More information2015 2nd Semester Exam Review
Algebra 2 2015 2nd Semester Exam Review 1. Write a function whose graph is a translation of the graph of the function in two directions. Describe the translation. 2. What are the solutions to the equation?
More informationPart 4: Exponential and Logarithmic Functions
Part 4: Exponential and Logarithmic Functions Chapter 5 I. Exponential Functions (5.1) II. The Natural Exponential Function (5.2) III. Logarithmic Functions (5.3) IV. Properties of Logarithms (5.4) V.
More informationFLC Ch 9. Ex 2 Graph each function. Label at least 3 points and include any pertinent information (e.g. asymptotes). a) (# 14) b) (# 18) c) (# 24)
Math 5 Trigonometry Sec 9.: Exponential Functions Properties of Exponents a = b > 0, b the following statements are true: b x is a unique real number for all real numbers x f(x) = b x is a function with
More informationMA Lesson 14 Notes Summer 2016 Exponential Functions
Solving Eponential Equations: There are two strategies used for solving an eponential equation. The first strategy, if possible, is to write each side of the equation using the same base. 3 E : Solve:
More informationGraphing Exponentials 6.0 Topic: Graphing Growth and Decay Functions
Graphing Exponentials 6.0 Topic: Graphing Growth and Decay Functions Date: Objectives: SWBAT (Graph Exponential Functions) Main Ideas: Mother Function Exponential Assignment: Parent Function: f(x) = b
More informationStudy Guide and Review - Chapter 7
Choose a word or term from the list above that best completes each statement or phrase. 1. A function of the form f (x) = b x where b > 1 is a(n) function. exponential growth 2. In x = b y, the variable
More informationExample. Determine the inverse of the given function (if it exists). f(x) = 3
Example. Determine the inverse of the given function (if it exists). f(x) = g(x) = p x + x We know want to look at two di erent types of functions, called logarithmic functions and exponential functions.
More informationGUIDED NOTES 6.1 EXPONENTIAL FUNCTIONS
GUIDED NOTES 6.1 EXPONENTIAL FUNCTIONS LEARNING OBJECTIVES In this section, you will: Evaluate exponential functions. Find the equation of an exponential function. Use compound interest formulas. Evaluate
More informationExponents and Logarithms Exam
Name: Class: Date: Exponents and Logarithms Exam Multiple Choice Identify the choice that best completes the statement or answers the question.. The decay of a mass of a radioactive sample can be represented
More information8.1 Apply Exponent Properties Involving Products. Learning Outcome To use properties of exponents involving products
8.1 Apply Exponent Properties Involving Products Learning Outcome To use properties of exponents involving products Product of Powers Property Let a be a real number, and let m and n be positive integers.
More informationfor every x in the gomain of g
Section.7 Definition of Inverse Function Let f and g be two functions such that f(g(x)) = x for every x in the gomain of g and g(f(x)) = x for every x in the gomain of f Under these conditions, the function
More informationWBHS Algebra 2 - Final Exam
Class: _ Date: _ WBHS Algebra 2 - Final Eam Multiple Choice Identify the choice that best completes the statement or answers the question. Describe the pattern in the sequence. Find the net three terms.
More informationExponential Functions and Their Graphs (Section 3-1)
Exponential Functions and Their Graphs (Section 3-1) Essential Question: How do you graph an exponential function? Students will write a summary describing the steps for graphing an exponential function.
More informationGUIDED NOTES 6.1 EXPONENTIAL FUNCTIONS
GUIDED NOTES 6.1 EXPONENTIAL FUNCTIONS LEARNING OBJECTIVES In this section, you will: Evaluate exponential functions. Find the equation of an exponential function. Use compound interest formulas. Evaluate
More informationExponential Growth. b.) What will the population be in 3 years?
0 Eponential Growth y = a b a b Suppose your school has 4512 students this year. The student population is growing 2.5% each year. a.) Write an equation to model the student population. b.) What will the
More informationExponential and Logarithmic Functions. Copyright Cengage Learning. All rights reserved.
3 Exponential and Logarithmic Functions Copyright Cengage Learning. All rights reserved. 3.1 Exponential Functions and Their Graphs Copyright Cengage Learning. All rights reserved. What You Should Learn
More informationTwo-Year Algebra 2 A Semester Exam Review
Semester Eam Review Two-Year Algebra A Semester Eam Review 05 06 MCPS Page Semester Eam Review Eam Formulas General Eponential Equation: y ab Eponential Growth: A t A r 0 t Eponential Decay: A t A r Continuous
More informationExponential and Logarithmic Modeling
Exponential and Logarithmic Modeling Multiple Choice Identify the choice that best completes the statement or answers the question. 1. An initial population of 505 quail increases at an annual rate of
More informationTopic 33: One-to-One Functions. Are the following functions one-to-one over their domains?
Topic 33: One-to-One Functions Definition: A function f is said to be one-to-one if for every value f(x) in the range of f there is exactly one corresponding x-value in the domain of f. Ex. Are the following
More information1. How many x-intercepts does the exponential function f(x) = 2(10) x have? B. 1 C. 2 D. 3
Multiple Choice 1. How many x-intercepts does the exponential function f(x) = 2(10) x have? A. 0 B. 1 C. 2 D. 3 2. How many y-intercepts does the exponential function f(x) = (5) x have? A. 0 B. 1 C. 2
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Calculus I - Homework Chapter 2 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the graph is the graph of a function. 1) 1)
More informationf(x) = d(x) q(x) + r(x).
Section 5.4: Dividing Polynomials 1. The division algorithm states, given a polynomial dividend, f(x), and non-zero polynomial divisor, d(x), where the degree of d(x) is less than or equal to the degree
More informationAlgebra 2 Honors: Final Exam Review
Name: Class: Date: Algebra 2 Honors: Final Exam Review Directions: You may write on this review packet. Remember that this packet is similar to the questions that you will have on your final exam. Attempt
More informationChapter 8 Prerequisite Skills
Chapter 8 Prerequisite Skills BLM 8. How are 9 and 7 the same? How are they different?. Between which two consecutive whole numbers does the value of each root fall? Which number is it closer to? a) 8
More informationIntermediate Algebra Final Exam Review
Intermediate Algebra Final Exam Review Note to students: The final exam for MAT10, MAT 11 and MAT1 will consist of 30 multiple-choice questions and a few open-ended questions. The exam itself will cover
More informationMath 180 Chapter 4 Lecture Notes. Professor Miguel Ornelas
Math 80 Chapter 4 Lecture Notes Professor Miguel Ornelas M. Ornelas Math 80 Lecture Notes Section 4. Section 4. Inverse Functions Definition of One-to-One Function A function f with domain D and range
More informationUnit 8: Exponential & Logarithmic Functions
Date Period Unit 8: Eponential & Logarithmic Functions DAY TOPIC ASSIGNMENT 1 8.1 Eponential Growth Pg 47 48 #1 15 odd; 6, 54, 55 8.1 Eponential Decay Pg 47 48 #16 all; 5 1 odd; 5, 7 4 all; 45 5 all 4
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) An initial investment of $14,000 is invested for 9 years in an account
More informationChapter 2 Functions and Graphs
Chapter 2 Functions and Graphs Section 5 Exponential Functions Objectives for Section 2.5 Exponential Functions The student will be able to graph and identify the properties of exponential functions. The
More informationMath 103 Intermediate Algebra Final Exam Review Practice Problems
Math 10 Intermediate Algebra Final Eam Review Practice Problems The final eam covers Chapter, Chapter, Sections 4.1 4., Chapter 5, Sections 6.1-6.4, 6.6-6.7, Chapter 7, Chapter 8, and Chapter 9. The list
More informationEXAM 3 Tuesday, March 18, 2003
MATH 12001 Precalculus: Algebra & Trigonometry Spring 2003 Sections 2 & 3 Darci L. Kracht Name: Score: /100. 115 pts available EXAM 3 Tuesday, March 18, 2003 Part I: NO CALCULATORS. (You must turn this
More information2.6 Logarithmic Functions. Inverse Functions. Question: What is the relationship between f(x) = x 2 and g(x) = x?
Inverse Functions Question: What is the relationship between f(x) = x 3 and g(x) = 3 x? Question: What is the relationship between f(x) = x 2 and g(x) = x? Definition (One-to-One Function) A function f
More information#2. Be able to identify what an exponential decay equation/function looks like.
1 Pre-AP Algebra II Chapter 7 Test Review Standards/Goals: G.2.a.: I can graph exponential and logarithmic functions with and without technology. G.2.b.: I can convert exponential equations to logarithmic
More informationFinal Exam Review: Study Guide Math 3
Final Exam Review: Study Guide Math 3 Name: Day 1 Functions, Graphing, Regression Relation: Function: Domain: Range: Asymptote: Hole: Graphs of Functions f(x) = x f(x) = f(x) = x f(x) = x 3 Key Ideas Key
More informationExploring the Logarithmic Function Pg. 451 # 1 6. Transformations of the Logarithmic Function Pg. 457 # 1 4, 7, 9
UNIT 7 EXPONENTIAL AND LOGARITHMIC FUNCTIONS Date Lesson Text TOPIC Homework Dec. 7. (70) 8. Exploring the Logarithmic Function Pg. 45 # 6 Dec. 4 7. (7) 8. Transformations of the Logarithmic Function Pg.
More informationReview of Functions A relation is a function if each input has exactly output. The graph of a function passes the vertical line test.
CA-Fall 011-Jordan College Algebra, 4 th edition, Beecher/Penna/Bittinger, Pearson/Addison Wesley, 01 Chapter 5: Exponential Functions and Logarithmic Functions 1 Section 5.1 Inverse Functions Inverse
More information9-3 CC6 Exponential Growth and and Decay
9-3 CC6 Exponential Growth and and Decay Application Graphs (transformation) Exponential v.s. Log Algebra 1 Warm Up Simplify each expression. 1. (4 + 0.05) 2 16.4025 2. 25(1 + 0.02) 3 26.5302 3. 1.0075
More informationIntroduction to Exponential Functions (plus Exponential Models)
Haberman MTH Introduction to Eponential Functions (plus Eponential Models) Eponential functions are functions in which the variable appears in the eponent. For eample, f( ) 80 (0.35) is an eponential function
More informationINTERNET MAT 117 Review Problems. (1) Let us consider the circle with equation. (b) Find the center and the radius of the circle given above.
INTERNET MAT 117 Review Problems (1) Let us consider the circle with equation x 2 + y 2 + 2x + 3y + 3 4 = 0. (a) Find the standard form of the equation of the circle given above. (b) Find the center and
More informationSolving Exponential Equations (Applied Problems) Class Work
Solving Exponential Equations (Applied Problems) Class Work Objective: You will be able to solve problems involving exponential situations. Quick Review: Solve each equation for the variable. A. 2 = 4e
More informationCollege Algebra and College Algebra with Review Final Review
The final exam comprises 30 questions. Each of the 20 multiple choice questions is worth 3 points and each of the 10 open-ended questions is worth 4 points. Instructions for the Actual Final Exam: Work
More informationAlgebra III: Blizzard Bag #1 Exponential and Logarithm Functions
NAME : DATE: PERIOD: Algebra III: Blizzard Bag #1 Exponential and Logarithm Functions Students need to complete the following assignment, which will aid in review for the end of course exam. Look back
More informationLogarithmic Functions
Logarithmic Functions Definition 1. For x > 0, a > 0, and a 1, y = log a x if and only if x = a y. The function f(x) = log a x is called the logarithmic function with base a. Example 1. Evaluate the following
More information8-1 Exploring Exponential Models
8- Eploring Eponential Models Eponential Function A function with the general form, where is a real number, a 0, b > 0 and b. Eample: y = 4() Growth Factor When b >, b is the growth factor Eample: y =
More informationSec. 4.2 Logarithmic Functions
Sec. 4.2 Logarithmic Functions The Logarithmic Function with Base a has domain all positive real numbers and is defined by Where and is the inverse function of So and Logarithms are inverses of Exponential
More information4.1 Exponential Functions
Chapter 4 Exponential and Logarithmic Functions 531 4.1 Exponential Functions In this section, you will: Learning Objectives 4.1.1 Evaluate exponential functions. 4.1.2 Find the equation of an exponential
More informationwhere is a constant other than ( and ) and
Section 12.1: EXPONENTIAL FUNCTIONS When you are done with your homework you should be able to Evaluate eponential functions Graph eponential functions Evaluate functions with base e Use compound interest
More informationMA Lesson 30 Exponential and Logarithmic Application Problems
MA 15200 Lesson 30 Exponential and Logarithmic Application Problems In order to solve the applied problems in this lesson, a student must know how to use the x log, ln, e, and power key functions on a
More informationShow that the set of ordered pairs (x, y) in the table below satisfied a quadratic relationship. Find. Think Pair Share
NAME: DATE: Algebra 2: Lesson 11-8 Exponential and Logarithmic Regression Learning Goals How do we write an equation that models an exponential or logarithmic function Warm Up Answer the following question
More informationAlgebra 2 Honors. Logs Test Review
Algebra 2 Honors Logs Test Review Name Date Let ( ) = ( ) = ( ) =. Perform the indicated operation and state the domain when necessary. 1. ( (6)) 2. ( ( 3)) 3. ( (6)) 4. ( ( )) 5. ( ( )) 6. ( ( )) 7. (
More informationMath 11A Graphing Exponents and Logs CLASSWORK Day 1 Logarithms Applications
Log Apps Packet Revised: 3/26/2012 Math 11A Graphing Eponents and Logs CLASSWORK Day 1 Logarithms Applications Eponential Function: Eponential Growth: Asymptote: Eponential Decay: Parent function for Eponential
More informationMAT 111 Final Exam Fall 2013 Name: If solving graphically, sketch a graph and label the solution.
MAT 111 Final Exam Fall 2013 Name: Show all work on test to receive credit. Draw a box around your answer. If solving algebraically, show all steps. If solving graphically, sketch a graph and label the
More information1. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y 3x
MATH 94 Final Exam Review. Graph each of the given equations, state the domain and range, and specify all intercepts and symmetry. a) y x b) y x 4 c) y x 4. Determine whether or not each of the following
More informationInverse Functions. Definition 1. The exponential function f with base a is denoted by. f(x) = a x
Inverse Functions Definition 1. The exponential function f with base a is denoted by f(x) = a x where a > 0, a 1, and x is any real number. Example 1. In the same coordinate plane, sketch the graph of
More informationName: 1. 2,506 bacteria bacteria bacteria bacteria. Answer: $ 5. Solve the equation
Name: Print Close During a lab experiment, bacteria are growing continuously at an exponential rate. The initial number of bacteria was 120, which increased to 420 after 5 days. If the bacteria continue
More information9.7 Common Logarithms, Natural Logarithms, and Change of Base
580 CHAPTER 9 Exponential and Logarithmic Functions Graph each function. 6. y = a x 2 b 7. y = 2 x + 8. y = log x 9. y = log / x Solve. 20. 2 x = 8 2. 9 = x -5 22. 4 x - = 8 x +2 2. 25 x = 25 x - 24. log
More informationAlgebra II Honors Final Exam Review
Class: Date: Algebra II Honors Final Exam Review Short Answer. Evaluate the series 5n. 8 n =. Evaluate the series (n + ). n = What is the sum of the finite arithmetic series?. 9+ + 5+ 8+ + + 59. 6 + 9
More information17 Exponential and Logarithmic Functions
17 Exponential and Logarithmic Functions Concepts: Exponential Functions Power Functions vs. Exponential Functions The Definition of an Exponential Function Graphing Exponential Functions Exponential Growth
More informationYou identified, graphed, and described several parent functions. (Lesson 1-5)
You identified, graphed, and described several parent functions. (Lesson 1-5) Evaluate, analyze, and graph exponential functions. Solve problems involving exponential growth and decay. algebraic function
More informationLecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions. Recall that a power function has the form f(x) = x r where r is a real number.
L7-1 Lecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions Recall that a power function has the form f(x) = x r where r is a real number. f(x) = x 1/2 f(x) = x 1/3 ex. Sketch the graph of
More informationAlgebra II CP Final Exam Review Packet. Calculator Questions
Name: Algebra II CP Final Exam Review Packet Calculator Questions 1. Solve the equation. Check for extraneous solutions. (Sec. 1.6) 2 8 37 2. Graph the inequality 31. (Sec. 2.8) 3. If y varies directly
More informationExponential Functions
Exponential Functions MATH 160, Precalculus J. Robert Buchanan Department of Mathematics Fall 2011 Objectives In this lesson we will learn to: recognize and evaluate exponential functions with base a,
More informationExponential Functions Dr. Laura J. Pyzdrowski
1 Names: (4 communication points) About this Laboratory An exponential function is an example of a function that is not an algebraic combination of polynomials. Such functions are called trancendental
More informationAlgebra 2, Spring Semester Review 2013
Class: Date: Algebra, Spring Semester Review 01 1. (1 point) Find the annual percent increase or decrease that y = 0.5(.) x models. 0% increase 0% decrease 10% increase d. 5% decrease. (1 point) An initial
More informationThe Exponential function f with base b is f (x) = b x where b > 0, b 1, x a real number
Chapter 4: 4.1: Exponential Functions Definition: Graphs of y = b x Exponential and Logarithmic Functions The Exponential function f with base b is f (x) = b x where b > 0, b 1, x a real number Graph:
More informationChapter 8. Exponential and Logarithmic Functions
Chapter 8 Eponential and Logarithmic Functions Lesson 8-1 Eploring Eponential Models Eponential Function The general form of an eponential function is y = ab. Growth Factor When the value of b is greater
More informationAlgebra 2 and Trigonometry Honors
Algebra 2 and Trigonometry Honors Chapter 8: Logarithms Part A Name: Teacher: Pd: 1 Table of Contents Day 1: Inverses and Graphs of Logarithmic Functions & Converting an Exponential Equation into a Logarithmic
More informationDay Date Assignment. 7.1 Notes Exponential Growth and Decay HW: 7.1 Practice Packet Tuesday Wednesday Thursday Friday
1 Day Date Assignment Friday Monday /09/18 (A) /1/18 (B) 7.1 Notes Exponential Growth and Decay HW: 7.1 Practice Packet Tuesday Wednesday Thursday Friday Tuesday Wednesday Thursday Friday Monday /1/18
More informationAlgebra II: Chapter 4 Semester Review Multiple Choice: Select the letter that best answers the question. D. Vertex: ( 1, 3.5) Max. Value: 1.
Algebra II: Chapter Semester Review Name Multiple Choice: Select the letter that best answers the question. 1. Determine the vertex and axis of symmetry of the. Determine the vertex and the maximum or
More informationf exist? Why or why not? Non-AP Calculus Summer Assignment 1. Use the graph at the right to answer the questions below. a. Find f (0).
1. Use the graph at the right to answer the questions below. 4 1 0 - - -1 0 1 4 5 6 7 8 9 10 11-1 - a. Find f (0). b. On what intervals is f( x) increasing? c. Find x so that f( x). d. Find the zeros of
More informationUnit 5: Exponential and Logarithmic Functions
71 Rational eponents Unit 5: Eponential and Logarithmic Functions If b is a real number and n and m are positive and have no common factors, then n m m b = b ( b ) m n n Laws of eponents a) b) c) d) e)
More informationEvaluate the expression using the values given in the table. 1) (f g)(6) x f(x) x g(x)
M60 (Precalculus) ch5 practice test Evaluate the expression using the values given in the table. 1) (f g)(6) 1) x 1 4 8 1 f(x) -4 8 0 15 x -5-4 1 6 g(x) 1-5 4 8 For the given functions f and g, find the
More informationA is any of ordered pairs. The set of all. components of the pairs is called the of the
Section 8.1: INTRODUCTION TO FUNCTIONS When you are done with your homework you should be able to Find the domain and range of a relation Determine whether a relation is a function Evaluate a function
More informationFinal Exam Review. Name: Class: Date: Short Answer
Name: Class: Date: ID: A Final Exam Review Short Answer. Use x, 2, 0,, 2 to graph the function f( x) 2 x. Then graph its inverse. Describe the domain and range of the inverse function. 2. Graph the inverse
More informationSection 4.4 Logarithmic and Exponential Equations
Section 4.4 Logarithmic and Exponential Equations Exponential Equations An exponential equation is one in which the variable occurs in the exponent. EXAMPLE: Solve the equation 2 x = 7. Solution 1: We
More informationCHAPTER 7. Logarithmic Functions
CHAPTER 7 Logarithmic Functions 7.1 CHARACTERISTICS OF LOGARITHMIC FUNCTIONS WITH BASE 10 AND BASE E Chapter 7 LOGARITHMS Logarithms are a new operation that we will learn. Similar to exponential functions,
More informationSummer MA Lesson 20 Section 2.7 (part 2), Section 4.1
Summer MA 500 Lesson 0 Section.7 (part ), Section 4. Definition of the Inverse of a Function: Let f and g be two functions such that f ( g ( )) for every in the domain of g and g( f( )) for every in the
More informationPolynomials and Rational Functions (2.1) The shape of the graph of a polynomial function is related to the degree of the polynomial
Polynomials and Rational Functions (2.1) The shape of the graph of a polynomial function is related to the degree of the polynomial Shapes of Polynomials Look at the shape of the odd degree polynomials
More informationGraphing Quadratic Functions 9.1
Quadratic Functions - Graphing Quadratic Functions 9.1 f ( x) = a x + b x + c (also called standard form). The graph of quadratic functions is called a parabola. Axis of Symmetry a central line which makes
More informationReview questions for Math 111 final. Please SHOW your WORK to receive full credit Final Test is based on 150 points
Please SHOW your WORK to receive full credit Final Test is based on 150 points 1. True or False questions (17 pts) a. Common Logarithmic functions cross the y axis at (0,1) b. A square matrix has as many
More informationAlgebra 2 & Trigonometry Honors Midterm Review 2016
Algebra & Trigonometry Honors Midterm Review 016 Solving Equations 1) Find all values of x that satisfy the equation, 5x 1 = x + 3 ) Solve the following by completing the square. Express your answer in
More informationExponential and Logarithmic Functions
Öğr. Gör. Volkan ÖĞER FBA 1021 Calculus 1/ 40 Exponential and Logarithmic Functions Exponential Functions The functions of the form f(x) = b x, for constant b, are important in mathematics, business, economics,
More information5.1. EXPONENTIAL FUNCTIONS AND THEIR GRAPHS
5.1. EXPONENTIAL FUNCTIONS AND THEIR GRAPHS 1 What You Should Learn Recognize and evaluate exponential functions with base a. Graph exponential functions and use the One-to-One Property. Recognize, evaluate,
More informationAlgebra 32 Midterm Review Packet
Algebra 2 Midterm Review Packet Formulas you will receive on the Midterm: y = a b x A = Pe rt A = P (1 + r n ) nt A = P(1 + r) t A = P(1 r) t x = b ± b2 4ac 2a Name: Teacher: Day/Period: Date of Midterm:
More informationAlgebra 2, Spring Semester Review
Class: Date: Algebra, Spring Semester Review 1. (1 point) Graph the relation and its inverse. Use open circles to graph the points of the inverse. x 0 4 9 10 y 3 7 1 a. c. b. d. 1 . (1 point) Is relation
More information4. Sketch the graph of the function. Ans: A 9. Sketch the graph of the function. Ans B. Version 1 Page 1
Name: Online ECh5 Prep Date: Scientific Calc ONLY! 4. Sketch the graph of the function. A) 9. Sketch the graph of the function. B) Ans B Version 1 Page 1 _ 10. Use a graphing utility to determine which
More information