Honors Algebra 2 ~ Spring 2014 Unit 6 ~ Chapter 8 Name Unit 6: Exponential & Logarithmic Functions NC Objectives: DAY DATE LESSON ASSIGNMENT

Size: px

Start display at page:

Download "Honors Algebra 2 ~ Spring 2014 Unit 6 ~ Chapter 8 Name Unit 6: Exponential & Logarithmic Functions NC Objectives: DAY DATE LESSON ASSIGNMENT"

Edwina Stone
5 years ago
Views:

Honors Algebra ~ Spring 0 Unit ~ Chapter 8 Name Unit : Eponential & Logarithmic Functions NC Objectives:.0 Simplify and perform operations with rational eponents and logarithms to solve problems.

Interpret the constants, coefficients, and bases in the contet of the problem..0 Create and use best-fit mathematical models of eponential functions to solve problems involving sets of data.

1 Honors Algebra ~ Spring 0 Unit ~ Chapter 8 Name Unit : Eponential & Logarithmic Functions NC Objectives:.0 Simplify and perform operations with rational eponents and logarithms to solve problems..0 Us the inverse of functions to model and solve problems..0 Use eponential functions to model and solve problems. a. Solve using tables, graphs, and algebraic properties. b. Interpret the constants, coefficients, and bases in the contet of the problem..0 Create and use best-fit mathematical models of eponential functions to solve problems involving sets of data. DAY DATE LESSON ASSIGNMENT Mon. April Tues. April Wed. April Eponential Models and Best Fit Packet p. & Section 8.: Properties of Eponential Functions Half-life, compound & continuous interest Quiz on Sections Section 8.: Logs & Logarithmic Functions as Inverses Packet p. (all) Packet p. #8- Packet p. #- Packet p. #0-7 Watch video: Thurs. April Section 8.: Properties of Logarithms Properties of Logs Handout ODD Problems Fri. April Finish Properties (LOG ) Packet p. # Mon. April 8 Tues. April 9 Review Sections 8. & 8. Packet Page 7 Study for Quiz on QUIZ on Sections Packet Page 8: Part A Section 8.: Solving Eponential & Log Equations Wed. April 0 Finish Section 8. Thurs. May Fri. May Mon. May Mon. May Section 8.: Natural Logarithms Application Problems Using Logs Application of Logs/Review Review for Unit Test Test is calculator active and inactive. Unit TEST (Chapter 8) Calculator Active and Inactive test Packet Page 8: Part B Packet page 9 Packet p. 0 Handout Packet p. STUDY FOR TEST Packet p. & Print notes & packet for unit 7 Chapter 9

2 Homework Section 8. I. Identify each function as modeling either eponential growth or eponential decay. What is the function s percent increase or decrease?. y = 98(.). y = 0.(.). y = (0.). (.7). y = (). y = (0.) 7. On their federal income ta returns, many self-employed individuals can depreciate the value of the business equipment they purchase. Suppose a computer valued at $00 depreciates at a rate of.% per year. After how many years is the value of the computer less than $000? II. Write an eponential function to model each situation. Find the value of the function after five years. 8. A population of 0 frogs increases at an annual rate of %. 9. A stock priced at $ increases at a rate of 7.% per year. 0. A $7,00 delivery van depreciates % each year.. A population of cougars decreases.% each year. III. Complete the following.. Todd says y = is an eponential function. Juan disagrees. Who is correct? Eplain.. Solve the following equations using the graphing calculator. a. =. b. 0.9 =. A herd of Tule Elk was introduced into the Point Reyes National Seashore in 978. The number of Elk present is a function of time. Year Pop a. Write a prediction equation to show how the number of Elk and the year are related. b. Predict the number of elk in 99. c. Estimate when there will be 77 Elk. A tractor that years ago cost $0,000, is now worth only $00. Find the average annual rate of depreciation.

3 Modeling Homework The data in the table give the average speed y (in knots) of the Trident motor yacht for several different engine speeds (in hundreds of revolutions per minute or RPMs). Engine Speed (in 00 s) Boat Speed a.) Find the linear model. Round to decimal places. b.) What is the R value?. a.) Find the quadratic model. Round to decimal places. b.) What is the R value?. a.) Find the cubic model. Round to decimal places. b.) What is the R value?. a.) Find the eponential model. Round to decimal places. b.) What is the R value?. Which model is the best?. Use the best model to estimate the speed of the Trident for an engine speed of 00 RPMs. *************************************************************************************************** 7. Find a linear, quadratic, and cubic model for the data. Use the model that best fits the data to estimate the diving record in 00. Men's Olympic Springboard Diving Records Year Points The best temperature to brew coffee is between 9 F and 0 F. Coffee is cool enough to drink at 8 F. The table shows temperature readings from a sample cup of coffee. How long does it take for a cup of coffee to be cool enough to drink? Use an eponential model. Time(min) Temp(F )

4 Homework Day : Half-life, compound and continuous interest Part

6 Use log 0.07 and log 0.8 to evaluate each epression. )log9 ) log ) log 0 ) log 0 0 ) log ) log. 9 Solve each equation. 7)log log 9 log 8) log 8 log w log ) log7 n log7 8 0) log y log log ) log 9(u ) log9 log9 u ) log7 log7 log7 log7 ) log log log 0 ) log ( ) log (7 0) ) log (9 ) log ( ) ) log 8( n ) log 8( n ) 7) log (m 7) log ( m ) log - log 8) log ( 8) log ( )

7 Evaluate:. log 8. log log 9 7. log 8 8. Review 8. & 8. LOGARITHMS!!! log. log. log 7 log 7 log log0 (log (log 9)) Epand using the properties of Logs: 0. log bc a log. 7 Write as a single logarithm with a coefficient of.. log a log b log c. (log log y ) 7 Evaluate: log.. 7 loga a. log log 7. log log 8. log log Given: log. 8 and log. find the following: 0. log 80. log 0.. log Solve.. log. log 8. log. log 7. log 8 8. log log 7 log 9. log log( ) 0. log( ) log( ). log. log 9. log ( ) log. log. log.. log 7. log ( ) 8. log (log log) 9. log 0. log7 ( ) log7 ( ) 8 7

8 Section 8. Homework: Solving Eponential Equations(PART:A) Use logarithms to solve each equation. y a ). 7.9 ) 8.. ) b+ ) 7. ) y log 78. ) k log 9.8 b b 7) 9 8) 7 9) 7c 9 8 0) 7 ) 7 ) 8 Section Homework(PART B) Use logarithms to solve each equation. Round to three decimal places.. 9 b =.. a- = =.. a- = a+. - =. y = 8 y- Solve each equation 7. e = 8 8. e = 0 9. ln ( ) = 0. e + = 0. e 7. ln ( + ) =. The function U(t) =.e.8t describes how the number of internet users, in millions, increased eponentially from 990 to 99. Let t represent the time, in years, since 990. a. What was the first year in which there were million internet users? b. How many years did it take for the number of users to double since 990? c. Solve the equation U =.e.8t for t.. Suppose $00 is invested at % annual interest compounded twice a year. When will the investment be worth $000?. An organism of a certain type can grow from 0 to 9 organisms in hours. Find k for the growth formula. Use: kt y ne.. A piece of machinery valued at $0,000 depreciates at % per year by the fied rate method. After how many years will the value have depreciated to $00,000? 7. A substance decomposes radioactively. Its half-life is years. Find the constant k in the decay formula. Use: kt y ne. 8

Assuming the interest rate is compounded continuously, what is the interest rate?.) Zeller industries bought some equipment for $0,000. It is epected to depreciate at a steady rate of 0% a year.

9 Compound Interest : n times a year n t More Practice FORMULAS: r A P Continuously Compounded : r t A Pe n Value of an Asset : V P( r) t Growth &/ Decay : k t y ne.) How long would it take for an investment of $00 to triple if it is invested in an account that earns % interest compounded quarterly..) Your bank promises to double your money in 8 years. Assuming the interest rate is compounded continuously, what is the interest rate?.) Zeller industries bought some equipment for $0,000. It is epected to depreciate at a steady rate of 0% a year. When will the value be half the original value?.) The Jameson's bought a new house for $,00 five years ago. The home is now worth $87,80. Assuming a steady rate of growth, what was the yearly rate of appreciation? ) You have inherited land that was purchased for $0,000 in 90. The value of the land increased by approimately % per year. a) Write a model for the value of the land t years after 90. b) What is the approimate value of the land in the year 00? c) At what year would the land be valued at about half a million dollars? ) Dave bought a new car 8 years ago for $800. To buy a new car comparably equipped now would cost $,00. Assuming a steady rate of increase, what was the yearly rate of inflation in car prices over the 8-year period? 7) An investment service promises to triple your money in years. Assuming continuous compounding of interest, what rate of interest is needed? 9

10 Homework Day 9 Solve each equation. Round answers to the nearest hundredth.. log log9. log log. log log. log log. log log. log( ). log( ) 7. log 8. log log Use natural logarithms to solve each equation. Round answers to the nearest hundredth.. e 0.. e 0. e. e 9. e ln. e Solve each equation. Check your answer. Round answers to the nearest hundredth.. ln( ) 7. ln(8 ) 7. ln ln. lne. ln. ln Write each epression as a natural logarithm.. ln - ln8. ln ln 9. aln lnb. lnz ln. ln ln. ln ln y 0

11 Unit ~ Chapter 8 Review. A population of 0 frogs increases at an annual rate of %. How many frogs are there after years?. A population of cougars decreases.% each year. How many cougars are left after 7 years?. Classify each function as modeling growth or decay. Then find the functions percent increase or decrease. a. f( ) (.8) b. f( ) (.). Graph the function: f( ). Write an equation in the form y ab with base, passing through (, 0).. Troy s parents started a savings account for him when he was born. They invested $00 in an account with 8% annual interest compounded quarterly. How much is in the account on his 8 th birthday? 7. Suppose you invest $00 at an annual interest rate of.% compounded continuously. Find the amount in the account after years. 8. Arsenic-7 is used to locate brain tumors. It has a half-life of 7. days. Write the eponential decay function of a 90-mg sample. Use the function to find the amount remaining after 8 days. 9. Write the equation form. 0. Write the equation 7 eponential form.. Evaluate: log. 8. Evaluate: log. 7 8in logarithmic log 89 in. Evaluate: log7.. Graph: ylog ( ). Graph: ylog ( ). Given log.87 and log8. find log Epand log ( ) 8. Epand log 9. Solve 7 0. Solve Solve 9. Solve log8log 9 log. Solve log ( ). Solve ln( 7). Solve e Solve log log log 7. Solve Solve 8 9. Use the change of base formula to find log The number of people in the Denver suburban area has grown eponentially since 90 according to the equation kt P P0 e. In 90 there were 0,000 people and in 90, there were 70,00. How many people lived in the Denver suburban area in 980?

12 Review Answers. 7 Unit ~ Chapter 8 Review - Answers. ; a) growth; 8%...0. b) decay; 8% y () $ $ log log( ) mg 8. log8 log log k Pop. in 980 =,8,08

13 .) Simplify 8 7 Cumulative Review!!!.) In 98, the population in Greensboro, N.C. was 97,90. Since then it has been growing at the Rate of.9% annually. What equation models the population t years after 98?.) Solve A. y 97,90(.0) t B. y 97,90( 9) t C. y 97,90(.9) t D. y 97,90(.09) t.) Solve : A. {} B., C. {-, } D..) If f() = - and g() =, what is f(g(-))? A. 7 B. C. D. 7.) Simplify: y y n 7.) Eactly 79 feet of wallpaper border were used to decorate around the ceiling of a rectangular room. To the nearest square foot, what is the maimum possible area of the room? A. 0 ft B. 0 ft C. 9 ft D. 90 ft 8.) Using y, what is when y = 8? 8 A. B. C. 8 D. 0 9.) Ellen deposited $00 in an account that pays % interest compounded continuously. How long will it take for her money to triple? A. 7.9 years B.. years C. 8. years D..0 years 0.) Solve ln e

14 .) Three years ago a house was bought for $9,000. Today it is worth $,000. Find the approimate yearly rate of appreciation. A. 7.% B..% C..8% D. % ( ).) Simplify: ( 9) A. B. ( ) C. ( ) D. ( ) 9.) Find an eponential function of the form y = ab whose graph passes through (, ) and (, 8)..) Solve..) Relative to the graph of y =, how could the graph of y = (-) + best be described? A. It shifts unit to the right and units down. B. It shifts unit to the right and units up. C. It shifts unit to the left and units down. D. It shifts unit to the left and units up..) Let f() = + and g() =. What is g(f())? A. + B. + C. 8 + D ) Divide 8 by. A. B. C. D. 8.) Solve: y = 8 + y = A. {(,). (,-), (-,), (-,-)} B. {(0,), (0,-)} C. {(,). (,-), (-,), (-,-)} D. {(,0), (,0)} 9.) Which equation best fits the data in the given table? # half-lives 0 Remaining,000,000, amount A. y,000 B. y,000 C. (000) y D. (000) y 0.) Solve 0. A. B. C. or D. or

Unit 8: Exponential & Logarithmic Functions

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