Math 10 Chapter 6.10: Solving Application Problems Objectives: Exponential growth/growth models Using logarithms to solve
|
|
|
- Rosamond Patrick
- 5 years ago
- Views:
Transcription
1 Math 10 Chapter 6.10: Solving Application Problems Objectives: Exponential growth/growth models Using logarithms to solve Exponential Growth Models Steps for Solving Application Problems: 1. Read, throw out nonsense numbers 2. Assign a variable (What is it asking for?) 3. Write an equation 4. Solve the equation 5. Check, does it make sense? An exponential equation or exponential function is of the form y = a x or f(x) = a x, where a > 0, a 1. Exponential Growth or Decay Formula: P( t) Pa, a 0, a 1 P 0 represents the original amount present, P(t) represents the amount present after t years, and a and k are constants. When a > 1, P(t) increases. (Growth) Ex: a = 2 When 0 < a < 1, P(t) decreases. (Decay) Ex: a = ½ Ex: The exponential graph below models the U.S. cellular telephone subscribership, P (t), in thousands, for t years 1989 through The formula a. Use the formula to calculate the number of subscribers in P ) t ( t) 3,500(1.257 models this growth. b. Use the formula to calculate the year it will be when the number of subscribers reaches 500,000 thousand.
2 You try: 1. The exponential graph below models the percentage of surface sunlight, f(x), that reaches a depth of x x feet beneath the surface of the ocean. The formula f ( x) 20(0.975) models this decay. a. Use the formula to calculate the percentage of surface sunlight intensity at a depth of 20 feet. b. Use the formula to calculate the depth needed to only have 1% of surface sunlight intensity. Natural Exponential Growth or Decay Formula: P( t) Pe Ex: The exponential graph below models the risk of having a car accident, R(x) (as a percentage), with respect to a person s blood alcohol concentration, x. The formula R 12.77x ( x) 6e models this growth. a. Use the formula to calculate the percent of risk of getting into a car accident for a person that has a blood alcohol concentration around b. Use the formula to calculate the blood alcohol concentration necessary to have a 100% risk of getting into a car accident.
3 Ex: The exponential graph below shows the number of people, P (t), in millions, in the U.S. age 65 and over, for t years starting in 1900, with projected figures for the year 2010 and beyond. The general formula P ( t) Pe models this growth. a. Use the graph to find the initial population, P 0. b. Substitute a point on the graph into the formula P( t) Pe to find the constant grow rate, k. c. Use P 0 and k to find the general formula P( t) Pe. d. Use the formula found in part c. to calculate the projected number of people in the U.S. age 65 and over in the year e. Use the formula found in part c. to find when the population of people in the U.S. age 65 and over will reach 100 million people.
4 You try: 1. T he exponential graph below shows the U.S. gross domestic product (GDP), the market value of all goods and services produced within the US, P (t), in billions, for t years between 1965 and The general formula P ( t) Pe models this growth. a. Use the graph to find the initial GDP, P b. Substitute a point on the graph into the formula P( t) Pe to find the constant grow rate, k. c. Use P 0 and k to find the general formula P( t) Pe d. Use the formula found in part c. to calculate the GDP in e. Use the formula found in part c. to find when the GDP will be $20,000 billion.
5 2. Plutonium-239, a radioactive material used in most nuclear reactors, decays exponentially. If there are originally 16 grams of plutonium-239, then the amount of plutonium-239, P(t), remaining after t years is modeled by the formula P( t) 16e, where k < 0, since the amount of plutonium decreases as time goes on. a. If approximately grams of plutonium-239 remain after 50,000 years, find the decay rate, k. And, state the function that models this case. b. How much plutonium will remain after 50 years? c. How long will it take to have only 2 grams remain?
6 3. Carbon-14, found in all living organisms, decays exponentially when the organism dies. If there are originally 16 grams of carbon-14, then the amount of carbon-14, P(t), remaining after t years is modeled by the formula P( t) 16e, where k < 0, since the amount of carbon decreases as time goes on. a. If approximately 8 grams of carbon-14 remain after 5,730 years, find the decay rate, k. And, state the function that models this case. b. How much carbon-14 will remain after 50 years? c. How long will it take to have only 2 grams remain?
Chapter 9: Solving Application Problems Objectives: Exponential growth/growth models Using logarithms to solve
Math I5ZB Chapter 9: Solving Application Problems Objectives: Exponential growth/growth models Using logarithms to solve Steps for Solving Appiication Problems: 1. Read, throw out nonsense numbers 2. Assign
Math 10 Chapter 6.10: Solving Application Problems Objectives: Exponential growth/growth models Using logarithms to solve
Math 10 Chapter 6.10: Solving Application Problems Objectives: Exponential growth/growth models Using logarithms to solve Exponential Growth Models Steps for Solving Application Problems: 1. Read, throw
MATH 236 ELAC FALL 2017 CA 10 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MATH 36 ELAC FALL 7 CA MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) In a certain country, the rate of increase of the population is proportional
SHORT ANSWER. Answer the question, including units in your answer if needed. Show work and circle your final answer.
Math 131 Group Review Assignment (5.5, 5.6) Print Name SHORT ANSWER. Answer the question, including units in your answer if needed. Show work and circle your final answer. Solve the logarithmic equation.
Math 1314 Lesson 7 Applications of the Derivative
Math 1314 Lesson 7 Applications of the Derivative Recall from Lesson 6 that the derivative gives a formula for finding the slope of the tangent line to a function at any point on that function. Example
Properties of Logarithms. Example Expand the following: The Power Rule for Exponents - (b m ) n = b mn. Example Expand the following: b) ln x
Properties of Logarithms The Product Rule for Exponents - b m b n = b m+n Example Expand the following: a) log 4 (7 5) log b MN = log b M + log b N b) log (10x) The Power Rule for Exponents - (b m ) n
Math 1314 Lesson 7 Applications of the Derivative. rate of change, instantaneous rate of change, velocity, => the derivative
Math 1314 Lesson 7 Applications of the Derivative In word problems, whenever it s anything about a: rate of change, instantaneous rate of change, velocity, => the derivative average rate of change, difference
MATH 236 ELAC FALL 2017 CA 9 NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
MATH 236 ELAC FALL 207 CA 9 NAME: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. ) 27 p 3 27 p 3 ) 2) If 9 t 3 4t 9-2t = 3, find t. 2) Solve the equation.
4.1 Exponential Functions. For Formula 1, the value of n is based on the frequency of compounding. Common frequencies include:
Hartfield MATH 2040 Unit 4 Page 1 4.1 Exponential Functions Recall from algebra the formulas for Compound Interest: Formula 1 For Discretely Compounded Interest 1 A t P r n nt Formula 2 Continuously Compounded
Section 4.5. Using Exponential Functions to Model Data
Section 4.5 Using Exponential Functions to Model Data Exponential Model, Exponential Related, Approximately Exponentially Related Using Base Multiplier Property to Find a Model Definition An exponential
MATH Section 4.1
MATH 1311 Section 4.1 Exponential Growth and Decay As we saw in the previous chapter, functions are linear if adding or subtracting the same value will get you to different coordinate points. Exponential
Applications of Exponential Functions
Applications of Exponential Functions MATH 151 Calculus for Management J. Robert Buchanan Department of Mathematics Spring 2014 Objectives After this lesson we will be able to solve problems involving
Chapter 8: Exponential Astonishment Lecture notes Math 1030 Section B
Section B.1: Doubling Time Definition of doubling time The time required for each doubling in exponential growth is called the doubling time. After a time t, an exponentially growing quantity with a doubling
College Algebra. Word Problems
College Algebra Word Problems Example 2 (Section P6) The table shows the numbers N (in millions) of subscribers to a cellular telecommunication service in the United States from 2001 through 2010, where
Independent Study Project: Chapter 4 Exponential and Logarithmic Functions
Name: Date: Period: Independent Study Project: Chapter 4 Exponential and Logarithmic Functions Part I: Read each section taken from the Algebra & Trigonometry (Blitzer 2014) textbook. Fill in the blanks
MAC Module 8 Exponential and Logarithmic Functions I. Rev.S08
MAC 1105 Module 8 Exponential and Logarithmic Functions I Learning Objectives Upon completing this module, you should be able to: 1. Distinguish between linear and exponential growth. 2. Model data with
MAC Module 8. Exponential and Logarithmic Functions I. Learning Objectives. - Exponential Functions - Logarithmic Functions
MAC 1105 Module 8 Exponential and Logarithmic Functions I Learning Objectives Upon completing this module, you should be able to: 1. Distinguish between linear and exponential growth. 2. Model data with
Section K MATH 211 Homework Due Friday, 8/30/96 Professor J. Beachy Average: 15.1 / 20. ), and f(a + 1).
Section K MATH 211 Homework Due Friday, 8/30/96 Professor J. Beachy Average: 15.1 / 20 # 18, page 18: If f(x) = x2 x 2 1, find f( 1 2 ), f( 1 2 ), and f(a + 1). # 22, page 18: When a solution of acetylcholine
Section Exponential Functions
121 Section 4.1 - Exponential Functions Exponential functions are extremely important in both economics and science. It allows us to discuss the growth of money in a money market account as well as the
Math Released Item Algebra 2. Radioactive Element Equations VH147862
Math Released Item 2018 Algebra 2 Radioactive Element Equations VH147862 Anchor Set A1 A9 With Annotations Prompt Score Description VH147862 Rubric Part A 1 Student response includes the following element.
Alg2H Ch6: Investigating Exponential and Logarithmic Functions WK#14 Date:
Alg2H Ch6: Investigating Exponential and Logarithmic Functions WK#14 Date: Purpose: To investigate the behavior of exponential and logarithmic functions Investigations For investigations 1 and 2, enter
Math 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
Review of Exponential Relations
Review of Exponential Relations Integrated Math 2 1 Concepts to Know From Video Notes/ HW & Lesson Notes Zero and Integer Exponents Exponent Laws Scientific Notation Analyzing Data Sets (M&M Lab & HW/video
The 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:
17 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
Review Example 3: Suppose that we know the revenues of a company each year since This information is given in the table below:
Math 1314 ONLINE Final Exam Review Review Example 1: Suppose 3 g( x) = x x 9x + 18. Find the zeros of the function. Review Example : Find any points where intersect. f ( x) = 1.45x 7.x 1.6 and g( x) =.84x
8.2 Logistic Functions
8.2 Logistic Functions NOTES Write your questions here! You start with 2 rabbits. Find -Rabbit population grows exponentially at a constant of 1.4 -Rabbit population doubles every month -Rabbit population
INTERNET 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
MA 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:
Notes for exponential functions The week of March 6. Math 140
Notes for exponential functions The week of March 6 Math 140 Exponential functions: formulas An exponential function has the formula f (t) = ab t, where b is a positive constant; a is the initial value
exponential function exponential growth asymptote growth factor exponential decay decay factor
exponential function exponential growth asymptote growth factor exponential decay decay factor Answer: Graph Exponential Growth Functions Graph of y = 4 x. State the domain and range. Domain = {all real
Exponential 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
An 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
Solutions to Problems and
Solutions to Problems 1.2.24 and 1.2.27 Will Johnson September 6, 2014 Since people asked me about these problems, I said I d write up some solutions. (27) A general power function looks like f(x) = cx
Lesson 6 Practice Problems
Name: Date: Lesson 6 Section 6.1: Writing Exponential Models 1. Complete the following table. Growth Rate as a % Growth Rate as a decimal Growth Factor 13% 0.13 1.13 21% 7% 0.20 0.05 1.25 1.075 2.03 2.
10.4 Half-Life. Investigation. 290 Unit C Radioactivity
.4 Half-Life Figure Pitchblende, the major uranium ore, is a heavy mineral that contains uranium oxides, lead, and trace amounts of other radioactive elements. Pierre and Marie Curie found radium and polonium
Honors 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
Section 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
a) Represent this information using one or more equations.
Appendix G: Solving Systems of Equations Often, you will be able to solve a problem that you are interested in by finding a solution for a single equation. More complicated problems may require you to
STAT 430/510 Probability Lecture 12: Central Limit Theorem and Exponential Distribution
STAT 430/510 Probability Lecture 12: Central Limit Theorem and Exponential Distribution Pengyuan (Penelope) Wang June 15, 2011 Review Discussed Uniform Distribution and Normal Distribution Normal Approximation
Name: Partners: PreCalculus. Review 5 Version A
Name: Partners: PreCalculus Date: Review 5 Version A [A] Circle whether each statement is true or false. 1. 3 log 3 5x = 5x 2. log 2 16 x+3 = 4x + 3 3. ln x 6 + ln x 5 = ln x 30 4. If ln x = 4, then e
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. You are planning on purchasing a new car and have your eye on a specific model. You know that
Chapter 6 Differential Equations and Mathematical Modeling. 6.1 Antiderivatives and Slope Fields
Chapter 6 Differential Equations and Mathematical Modeling 6. Antiderivatives and Slope Fields Def: An equation of the form: = y ln x which contains a derivative is called a Differential Equation. In this
Unit 3 NOTES Honors Math 2 21
Unit 3 NOTES Honors Math 2 21 Warm Up: Exponential Regression Day 8: Point Ratio Form When handed to you at the drive-thru window, a cup of coffee was 200 o F. Some data has been collected about how the
Section 2.3: Logarithmic Functions Lecture 3 MTH 124
Procedural Skills Learning Objectives 1. Build an exponential function using the correct compounding identifiers (annually, monthly, continuously etc...) 2. Manipulate exponents algebraically. e.g. Solving
Logarithmic, Exponential, and Other Transcendental Functions. Copyright Cengage Learning. All rights reserved.
5 Logarithmic, Exponential, and Other Transcendental Functions Copyright Cengage Learning. All rights reserved. 5.5 Bases Other Than e and Applications Copyright Cengage Learning. All rights reserved.
nt and A = Pe rt to solve. 3) Find the accumulated value of an investment of $10,000 at 4% compounded semiannually for 5 years.
Exam 4 Review Approximate the number using a calculator. Round your answer to three decimal places. 1) 2 1.7 2) e -1.4 Use the compound interest formulas A = P 1 + r n nt and A = Pe rt to solve. 3) Find
Unit #1 - Transformation of Functions, Exponentials and Logarithms
Unit #1 - Transformation of Functions, Exponentials and Logarithms Some problems and solutions selected or adapted from Hughes-Hallett Calculus. Note: This unit, being review of pre-calculus has substantially
7-6 Growth and Decay. Let t = 7 in the salary equation above. So, Ms. Acosta will earn about $37, in 7 years.
1. SALARY Ms. Acosta received a job as a teacher with a starting salary of $34,000. According to her contract, she will receive a 1.5% increase in her salary every year. How much will Ms. Acosta earn in
UNIT 2 DERIVATIVES 2.1 EXPONENTIAL AND LOGARITHMIC FUNCTION APPLICATIONS. Pre-Class:
1830 UNIT 2 DERIVATIVES 2.1 EXPONENTIAL AND LOGARITHMIC FUNCTION APPLICATIONS Pre-Class: Take notes on the videos and readings (use the space below). Work and check problem #1 in the 2.1 NOTES section.
MULTIPLE 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
EXPONENTIAL, LOGARITHMIC, AND TRIGONOMETRIC FUNCTIONS
Calculus for the Life Sciences nd Edition Greenwell SOLUTIONS MANUAL Full download at: https://testbankreal.com/download/calculus-for-the-life-sciences-nd-editiongreenwell-solutions-manual-/ Calculus for
weebly.com/ Core Mathematics 3 Exponentials and Natural Logarithms
http://kumarmaths. weebly.com/ Core Mathematics 3 Exponentials and Natural Logarithms Core Maths 3 Exponentials and natural Logarithms Page 1 Ln and Exponentials C3 Content By the end of this unit you
GUIDED 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
f(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
Math 095 Final Exam Review - MLC
Math 095 Final Exam Review - MLC Although this is a comprehensive review, you should also look over your old reviews from previous modules, the readings, and your notes. Round to the thousandth unless
Page 1 of 10 MATH 120 Final Exam Review
Page 1 of 1 MATH 12 Final Exam Review Directions Part 1: Calculators will NOT be allowed on this part of the final exam. Unless the question asks for an estimate, give exact answers in completely reduced
Concept Category 2. Exponential and Log Functions
Concept Category 2 Exponential and Log Functions Concept Category 2 Check List *Find the inverse and composition of functions *Identify an exponential from a table, graph and equation *Identify the difference
Math 137 Exam #3 Review Guide
Math 7 Exam # Review Guide The third exam will cover Sections.-.6, 4.-4.7. The problems on this review guide are representative of the type of problems worked on homework and during class time. Do not
UNIT 5: DERIVATIVES OF EXPONENTIAL AND TRIGONOMETRIC FUNCTIONS. Qu: What do you remember about exponential and logarithmic functions?
UNIT 5: DERIVATIVES OF EXPONENTIAL AND TRIGONOMETRIC FUNCTIONS 5.1 DERIVATIVES OF EXPONENTIAL FUNCTIONS, y = e X Qu: What do you remember about exponential and logarithmic functions? e, called Euler s
1. The inaugural attendance of an annual music festival is 150,000. The attendance increases by 8% each year.
NAME: DATE: Algebra 2: Lesson 11 7 Writing Exponential Growth and Decay Functions Learning Goals 1. How can we write an exponential growth/decay equation and define its variables? DO NOW: Answer the following
a. If the vehicle loses 12% of its value annually, it keeps 100% - 12% =? % of its value. Because each year s value is a constant multiple of
Lesson 9-2 Lesson 9-2 Exponential Decay Vocabulary exponential decay depreciation half-life BIG IDEA When the constant growth factor in a situation is between 0 and 1, exponential decay occurs. In each
MATH 120 Elementary Functions Test #2
MATH 120 Elementary Functions Test #2 There are two forms of the test; both are included below. 1. [20 points] Find the domain and range of the function f ( x ) = log( 25 x 2 ). Sketch a graph of the curve
Final Exam Study Aid
Math 112 Final Exam Study Aid 1 of 33 Final Exam Study Aid Note: This study aid is intended to help you review for the final exam. It covers the primary concepts in the course, with a large emphasis on
Applications of Exponential Equations and Logarithms
Name: Date: Block: Applications of Exponential Equations and Logarithms DIRECTIONS: Write problem information. Show equations used for solving. Round final answers according to the situation. Label your
Chapter 6A Solving Exponential and Logarithmic Equations. Solve x+5 = x = 9 x x 2 = x 4. 5 x = 18
Fry Texas A&M University!! Math 150!! Chapter 6!! Fall 2014! 1 Chapter 6A Solving Exponential and Logarithmic Equations Solve 1. 4 3x+5 = 16 2. 3 x = 9 x+5 3. 8 x 2 = 1 4 5 9 x 4. 5 x = 18 Fry Texas A&M
Section 6.8 Exponential Models; Newton's Law of Cooling; Logistic Models
Section 6.8 Exponential Models; Newton's Law of Cooling; Logistic Models 197 Objective #1: Find Equations of Populations that Obey the Law of Uninhibited Growth. In the last section, we saw that when interest
Exponential 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,
EXPONENTS AND LOGS (CHAPTER 10)
EXPONENTS AND LOGS (CHAPTER 0) POINT SLOPE FORMULA The point slope formula is: y y m( ) where, y are the coordinates of a point on the line and m is the slope of the line. ) Write the equation of a line
Math 1101 Test 2 Practice Problems
Math 1101 Test 2 Practice Problems These problems are not intended to cover all possible test topics. These problems should serve as on activity in preparing for your test, but other study is required
Chapter 6: Exponential and Logarithmic Functions
Section 6.1: Algebra and Composition of Functions #1-9: Let f(x) = 2x + 3 and g(x) = 3 x. Find each function. 1) (f + g)(x) 2) (g f)(x) 3) (f/g)(x) 4) ( )( ) 5) ( g/f)(x) 6) ( )( ) 7) ( )( ) 8) (g+f)(x)
Concept Category 2. Exponential and Log Functions
Concept Category 2 Exponential and Log Functions Concept Category 2 Check List *Find the inverse and composition of functions *Identify an exponential from a table, graph and equation *Identify the difference
Lesson 26: Problem Set Sample Solutions
Problem Set Sample Solutions Problems and 2 provide students with more practice converting arithmetic and geometric sequences between explicit and recursive forms. Fluency with geometric sequences is required
INTERNET MAT 117. Solution for the Review Problems. (1) Let us consider the circle with equation. x 2 + 2x + y 2 + 3y = 3 4. (x + 1) 2 + (y + 3 2
INTERNET MAT 117 Solution for the 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. (i) Group
GUIDED 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
MATH-AII Algebra II - Unit 4 Test Exam not valid for Paper Pencil Test Sessions
MATH-AII Algebra II - Unit 4 Test Exam not valid for Paper Pencil Test Sessions [Exam ID:1087YR 1 Which of the following functions does NOT have a range of only the real numbers greater than or equal to
Unit 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
Study Island. 1. The table below represents a linear situation. x f(x)
Study Island Copyright 2014 Edmentum - All rights reserved. 4. A company is holding a dinner reception in a hotel ballroom. The graph represents the total cost of the ballroom rental and dinner. 1. The
date: math analysis 2 chapter 18: curve fitting and models
name: period: date: math analysis 2 mr. mellina chapter 18: curve fitting and models Sections: 18.1 Introduction to Curve Fitting; the Least-Squares Line 18.2 Fitting Exponential Curves 18.3 Fitting Power
AP Statistics Bivariate Data Analysis Test Review. Multiple-Choice
Name Period AP Statistics Bivariate Data Analysis Test Review Multiple-Choice 1. The correlation coefficient measures: (a) Whether there is a relationship between two variables (b) The strength of the
Math 1101 Exam 3 Practice Problems
Math 1101 Exam 3 Practice Problems These problems are not intended to cover all possible test topics. These problems should serve as an activity in preparing for your test, but other study is required
Half Life Introduction
Name: Date: Period: Half Life Introduction The half-life of an element is the time it will take half of the parent atoms to transmutate into different atoms (through alpha or beta decays, or another process).
Solutions. .5 = e k k = ln(.5) Now that we know k we find t for which the exponential function is = e kt
MATH 1220-03 Exponential Growth and Decay Spring 08 Solutions 1. (#15 from 6.5.) Cesium 137 and strontium 90 were two radioactive chemicals released at the Chernobyl nuclear reactor in April 1986. The
5.6 Applications and Models: Exponential Growth and Decay
5.6 Applications and Models: Exponential Growth and Decay Many natural (and business/financial) processes build on themselves exponentially. We will see several examples. All of these examples are functions
Intermediate 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
Math 611b Assignment #6 Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Math 611b Assignment #6 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find a formula for the function graphed. 1) 1) A) f(x) = 5 + x, x < -
Limits at Infinity. Horizontal Asymptotes. Definition (Limits at Infinity) Horizontal Asymptotes
Limits at Infinity If a function f has a domain that is unbounded, that is, one of the endpoints of its domain is ±, we can determine the long term behavior of the function using a it at infinity. Definition
Honors Math 2 Unit 5 Exponential Functions. *Quiz* Common Logs Solving for Exponents Review and Practice
Honors Math 2 Unit 5 Exponential Functions Notes and Activities Name: Date: Pd: Unit Objectives: Objectives: N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of
Assignment #3; Exponential Functions
AP Calculus Assignment #3; Exponential Functions Name: The equation identifies a family of functions called exponential functions. Notice that the ratio of consecutive amounts of outputs always stay the
Math 102- Final examination University of British Columbia December 14, 2012, 3:30 pm to 6:00 pm
Math 102- Final examination University of British Columbia December 14, 2012, 3:30 pm to 6:00 pm Name (print): ID number: Section number: This exam is closed book. Calculators or other electronic aids
Section 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
Part I: Multiple Choice Questions
Name: Part I: Multiple Choice Questions. What is the slope of the line y=3 A) 0 B) -3 ) C) 3 D) Undefined. What is the slope of the line perpendicular to the line x + 4y = 3 A) -/ B) / ) C) - D) 3. Find
1. Does each pair of formulas described below represent the same sequence? Justify your reasoning.
Lesson Summary To model exponential data as a function of time: Examine the data to see if there appears to be a constant growth or decay factor. Determine a growth factor and a point in time to correspond
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MAC 1105 Fall 2007 - Final Exam Dr. Schnackenberg If you do not agree with the given answers, answer "E" for "None of the above". MULTIPLE CHOICE. Choose the one alternative that best completes the statement
Review 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
1 Functions And Change
1 Functions And Change 1.1 What Is a Function? * Function A function is a rule that takes certain numbers as inputs and assigns to each a definite output number. The set of all input numbers is called
CHAPTER FIVE. Solutions for Section 5.1. Skill Refresher. Exercises
CHAPTER FIVE 5.1 SOLUTIONS 265 Solutions for Section 5.1 Skill Refresher S1. Since 1,000,000 = 10 6, we have x = 6. S2. Since 0.01 = 10 2, we have t = 2. S3. Since e 3 = ( e 3) 1/2 = e 3/2, we have z =
(MATH 1203, 1204, 1204R)
College Algebra (MATH 1203, 1204, 1204R) Departmental Review Problems For all questions that ask for an approximate answer, round to two decimal places (unless otherwise specified). The most closely related
Modeling with Exponential Functions
CHAPTER Modeling with Exponential Functions A nautilus is a sea creature that lives in a shell. The cross-section of a nautilus s shell, with its spiral of ever-smaller chambers, is a natural example of
Semester 2 Final Exam Review Guide for AMS I
Name: Semester 2 Final Exam Review Guide for AMS I Unit 4: Exponential Properties & Functions Lesson 1 Exponent Properties & Simplifying Radicals Products of Powers: when two powers with the same base