Small Investment, Big Reward

Transcription

1 Lesson 1.1 Skills Practice Name Date Small Investment, Big Reward Eponential Functions Vocabular Define each term in our own words. 1. eponential function 1. half-life Problem Set Write the eplicit formula for each geometric sequence. Then, use the equation to determine the 1 th term. Round answers to the nearest thousandth, if necessar ,15 9,15 a n 5 5? 3 n1 a 1 5 5? ? , Chapter 1 Skills Practice 7

2 Lesson 1.1 Skills Practice page Chapter 1 Skills Practice

3 Lesson 1.1 Skills Practice page 3 Name Date Write an eponential function in general form to represent each geometric sequence. Evaluate the function for the given value of n. Round to the nearest thousandth, if necessar. 7. a n 5?.5 n1 n 5 1 f(n) 5?.5 n1 5?.5 n? ( 5 ) 1 5?.5 n? ?.5 n f(1) 5 1.?.5 1 < 15,5.79. a n 5.3? n1 n a n 5 15?. n1 n 5 1. a n 5.5? 1.5 n1 n 5 Chapter 1 Skills Practice 9

4 Lesson 1.1 Skills Practice page 11. a n 5 1? n1 n a n 5 1?.5 n1 n Write an eponential function A(t), where t represents elapsed time, to represent each half-life situation. Then, use the function to complete each table. Round as necessar. 13. Elapsed Time (hours) Drug in Bloodstream (mg) Number of Half-Life Ccles A(t) 5 1 ( 1 A() 5 1 ( 1 t ) ) 5 1 ( 1 ) 1 < Elapsed Time (minutes) Bacteria Subject to Growth Inhibitor 1 5 Number of Half-Life Ccles Chapter 1 Skills Practice

5 Lesson 1.1 Skills Practice page 5 Name Date 15. Elapsed Time (ears) Strontium in Rock Sample (grams) 1 1 Number of Half-Life Ccles Elapsed Time (ears) 5,7 11, 15,75 17,1, C-1 in Rock Sample (grams) Number of Half-Life Ccles 1 3 Chapter 1 Skills Practice 31

6 Lesson 1.1 Skills Practice page 17. Elapsed Time (Das) 1 1 Rat Population Eposed to Virus Number of Half-Life Ccles Elapsed Time (Hours) 1 Participants in Tennis Tournament Number of Half-Life Ccles Chapter 1 Skills Practice

7 Lesson 1. Skills Practice Name Date We Have Liftoff! Properties of Eponential Graphs Vocabular Eplain how the natural base e is similar to and different from p. 1 Problem Set Determine whether the given function represents eponential growth or deca. Eplain our reasoning. 1. f() 5. f() 5. The function represents eponential growth because the base is greater than f() 5 ( 5 ). f() f() 5 ( 1 ). f() Chapter 1 Skills Practice 33

8 Lesson 1. Skills Practice page Complete each table and graph the eponential function. 7. f() 5 1 f() f() 5 ( 1 ) f() Chapter 1 Skills Practice

9 Lesson 1. Skills Practice page 3 Name Date 9. f() f() f() 5 ( 5 ) f() 1 1 Chapter 1 Skills Practice 35

10 Lesson 1. Skills Practice page 11. f() 5 f() f() 5.3 f() Chapter 1 Skills Practice

11 Lesson 1. Skills Practice page 5 Name Date Write an eponential function with the given characteristics. 13. increasing over (`, `) 1. decreasing over (`, `) reference point ( 1, 1 9 ) reference point ( 1, 3 ) Answers will var. f() as `, f() 15. end behavior: as `, f() ` 1. decreasing over (`, `) reference point (,.5) reference point (, 1) as `, f() ` 17. increasing over (`, `) 1. end behavior: as `, f() reference point ( 3, 1 ) reference point (, 1 1 ) Chapter 1 Skills Practice 37

12 Lesson 1. Skills Practice page Use the formula for compound interest to determine the amount of mone in each account after interest is accrued An investor deposits $1, in an account that promises an annual interest rate of 5%, compounded at the end of each ear. How much will be in the account after seven ears? There will be $1,7.1 in the account after seven ears. A(t) 5 P( r 1 1 n ) n? t A(7) 5 1, ( ?7 ) 1 5 1,(1.5) 7 < 1,7.1. At the start of the school ear, Fairview High School deposits PTA dues in an account that offers an annual interest rate of 3.5%, compounded at the end of each ear. If $5 is collected in PTA dues, how much mone will the school have at the start of the net school ear? 1. Kle put $3 of his birthda mone in the bank. The bank offers an annual interest rate of %, compounded twice a ear. How much mone will Kle have after three ears? 3 Chapter 1 Skills Practice

13 Lesson 1. Skills Practice page 7 Name Date. An investing group has $5, to invest. The put the mone in an account that has an annual interest rate of %, compounded monthl. How much mone will the group have at the end of 1 ears? 1 3. Interest is compounded quarterl at Mone Bank at an annual rate of 5.5%. A new client opens an account with $7. How much mone will be in the account at the end of si ears?. Sasha wants to earn the maimum interest on her mone. She decides to deposit $5 in two different banks for 9 das (3 months) to compare them before she deposits all of her mone. She finds a bank that compounds interest dail at an annual rate of.% and another bank that compounds interest monthl at an annual rate of.%. With which bank will she earn more mone? Chapter 1 Skills Practice 39

14 Lesson 1. Skills Practice page Use the formula for population growth to predict the population of each cit. 5. The population of Austin, Teas is growing at a rate of 3.9% per ear. If the population in 1 was approimatel 79,, what is the predicted population for 15? The population of Austin, Teas will be about 9,9 in 15. N(t) 5 N o e rt N(5) 5 79,e (.39? 5) 5 79,e.195 < 9,9 1. The population of Boston, Massachusetts is growing at a rate of 1.% annuall. The population in 13 was approimatel 3,5. What is the predicted population for 5? 7. The population of Charlotte, North Carolina in 13 was approimatel 775,. If the annual rate of growth is about 3.%, what is an approimation of Charlotte s population in? Chapter 1 Skills Practice

15 Lesson 1. Skills Practice page 9 Name Date. The population of Beijing, China in 1 was approimatel,9, and is growing at an annual rate of about 5.5%. What is an approimation of Beijing s population in 19? 1 9. The population of Detroit, Michigan is decreasing at an annual rate of about.75%. Detroit s population in 13 was approimatel 7,. What is the predicted population for 15? 3. The population of Berlin, German was about 3,9, in 11. Its population is declining at an annual rate of about.%. What is the predicted population for 5? Chapter 1 Skills Practice 1

16 1 Chapter 1 Skills Practice

17 Lesson 1.3 Skills Practice Name Date I Like to Move It Transformations of Eponential Functions Problem Set Complete the table to determine the corresponding points on c(), given reference points on f(). Then, graph c() on the same coordinate plane as f() and state the domain, range, and asmptotes of c(). 1. f() 5 c() 5 f( 1) Reference Points on f() Corresponding Points on c() ( 1, 1 ) (, 1 ) f() c() 1 (, 1) (1, 1) (1, ) (, ) Domain: All real numbers Range:. Horizontal asmptote: 5. f() 5 c() 5 f() Reference Points on f() ( 1, 1 ) (, 1) (1, ) Corresponding Points on c() f() Domain: Range: Horizontal asmptote: Chapter 1 Skills Practice 3

18 Lesson 1.3 Skills Practice page 3. f() 5 3 c() 5 f(3) Reference Points on f() Corresponding Points on c() f() ( 1, 1 3 ) (, 1) (1, 3) 1 Domain: Range: Horizontal asmptote:. f() 5 c() 5 f() Reference Points on f() Corresponding Points on c() ( 1, 1 ) (, 1) f() (1, ) Domain: Range: Horizontal asmptote: Chapter 1 Skills Practice

19 Lesson 1.3 Skills Practice page 3 Name Date 5. f() 5 5 c() 5 f( 1 3) Reference Points on f() ( 1, 1 5 ) Corresponding Points on c() (, 1) (1, 5) f() 1 Domain: Range: Horizontal asmptote:. f() 5 c() 5 f() 1 Reference Points on f() Corresponding Points on c() ( 1, 1 ) f() (, 1) (1, ) Domain: Range: Horizontal asmptote: Chapter 1 Skills Practice 5

20 Lesson 1.3 Skills Practice page Describe the transformations performed on f() to create g(). Then, write an equation for g() in terms of f(). 7. f() g() 1 ( 1, ) (1, ) (, 1) 1 3 (, ) 1 (, 3) (, ) 1 1 To create g(), the graph of f() is compressed horizontall b a factor of and verticall translated up 1 unit. g() 5 f() 1 1. f() g() (1, ) (, ) 1 ( 1, ) (, 1) ( 3, 1) 1 (, ) Chapter 1 Skills Practice

21 Lesson 1.3 Skills Practice page 5 Name Date 9. f() (1, 5) 1 ( 1, ) 5 (, 1) (, ) ( 1, ) 5 (1, ) g() 1 1. f() g() 1 ( 1, ) 3 (1, 3) (, 1) ( 1, 3) (, 1) (, 3 ) 3 Chapter 1 Skills Practice 7

22 Lesson 1.3 Skills Practice page 11. f() 1 g() (1, ) ( 1, ) (, 1) 1 (, 1) (, ) 3 (, ) 1. f() g() ( 1, 1) (1, 5) (, ) 1 ( 1, ) 5 (, 1) 1 (1, 5 ) 5 Chapter 1 Skills Practice

23 Lesson 1.3 Skills Practice page 7 Name Date Describe the transformations performed on m() that produced t(). Then, write an eponential equation for t() m() t() 5 m( 1 1) The graph of the function m() is reflected over the -ais and horizontall translated left 1 unit to produce t(). t() m() 5 5 t() 5 3m() 15. m() 5 e t() 5 1 m() 1 1. m() 5 t() 5 m(3 1) Chapter 1 Skills Practice 9

24 Lesson 1.3 Skills Practice page 17. m() 5 7 t() 5 m(.5 1 ) 1 1. m() 5 t() 5 m() Chapter 1 Skills Practice

25 Lesson 1. Skills Practice Name Date I Feel the Earth Move Logarithmic Functions Vocabular Write the term that best completes each sentence. logarithm logarithmic function common logarithm natural logarithm 1. The of a number for a given base is the eponent to which 1 the base must be raised in order to produce that number.. A is a logarithm with base e, and is usuall written as ln. 3. A is a function involving a logarithm.. A is a logarithm with a base 1 and is usuall written without a base specified. Problem Set Write each eponential equation as a corresponding logarithmic equation log 3 (9) , 5. ( 1 ) ( 1 11 ) 5 11 Chapter 1 Skills Practice 51

26 Lesson 1. Skills Practice page Write each logarithmic equation as a corresponding eponential equation. 7. log 7 ( 1 9 ) 5. log ( ) 5 9. log (1) log ( 1 19 ) log 1 ( ) log(79) Graph the inverse of each eponential function f(). Then, describe the domain, range, asmptotes, and end behavior of the inverse. 13. f() f() 5 f() f() f 1 () Domain:. Range: All real numbers Domain: Range: Asmptotes: 5 Asmptotes: End behavior: As, `. End behavior: As 1`, 1`. 5 Chapter 1 Skills Practice

27 Lesson 1. Skills Practice page 3 Name Date 15. f() f() 5 f() f() 1 Domain: Range: Asmptotes: End behavior: Domain: Range: Asmptotes: End behavior: Chapter 1 Skills Practice 53

28 Lesson 1. Skills Practice page 17. f() 5 e 1. f() 5 5 f() f() 1 Domain: Range: Asmptotes: End behavior: Domain: Range: Asmptotes: End behavior: Solve each logarithmic equation log 9 ( 1 1 b )..93 <? log (.5) b b 1 b log (3)..39 < log b n 3..5 < ln z log ( g 1 ) 5 Chapter 1 Skills Practice

29 Lesson 1.5 Skills Practice Name Date More Than Meets the Ee Transformations of Logarithmic Functions Problem Set Analze the graphs of f() and g(). Describe the transformations performed on the graph of f() to produce the graph of the transformed function g(). Then, write an equation for g(). 1.. g() 1 f() = log () f() = log 3 () g() The graph of g() was horizontall translated right units to produce the graph of g(). g() 5 log ( ) Chapter 1 Skills Practice 55

30 Lesson 1.5 Skills Practice page 3.. g() f() = log () f() = log 5 () g() 1 5. g(). g() f() = log () f() = log () 5 Chapter 1 Skills Practice

31 Lesson 1.5 Skills Practice page 3 Name Date The graph of f() 5 log () is shown. Use the graph of f() to sketch the transformed function m() on the coordinate plane. Then, state the domain, range and asmptotes of m(). 7. m() 5 f() 1. Domain of m(): (, `) Range of m(): (`, `) Asmptote of m(): 5 m() 5 f() 1 f() 5 log() 1. m() 5 f( ). Domain of m(): Range of m(): f() 5 log() Asmptote of m(): Chapter 1 Skills Practice 57

32 Lesson 1.5 Skills Practice page 9. m() 5 f( 1 1) 3. Domain of m(): Range of m(): f() 5 log() Asmptote of m(): 1 1. m() 5 f( 3). Domain of m(): Range of m(): f() 5 log() Asmptote of m(): 5 Chapter 1 Skills Practice

33 Lesson 1.5 Skills Practice page 5 Name Date 11. m() 5.5f() 1 1. Domain of m(): Range of m(): f() 5 log() Asmptote of m(): 1 1. m() 5 f( ) 1 Domain of m(): Range of m(): Asmptote of m(): f() 5 log() Chapter 1 Skills Practice 59

34 Lesson 1.5 Skills Practice page Write a transformed logarithmic function, c(), in terms of f() 5 log () with the characteristics given. 13. vertical asmptote at 5 1. domain of (`, 3) Answers will var. c() 5 f ( ) Reference Points on f() Corresponding Points on c() 1. vertical asmptote at 5 ( 1, 1 ) ( 1, 3 ) (1, ) (1, ) (, 1) (, 3) 17. domain: (, `) 1. point: (5, ) Reference Points on f() Corresponding Points on c() ( 1, 1 ) ( 1, 3 ) (1, ) (1, ) (, 1) (, 1) Chapter 1 Skills Practice

35 Lesson 1.5 Skills Practice page 7 Name Date Consider the function 5 f() and the transformed function g(). Write an equation for g 1 () in terms of f 1 (). 19. g() 5 f() 1 3. g() 5 f( ) g 1 () 5 f 1 ( 3) 1. g() 5 f( 1 ). g() 5 f() g() 5 f( 1 1) 3. g() 5 f( ) 1 Consider the function f() 5 and its inverse function f 1 () 5 log (). Complete a table for each transformation and write the transformation function in terms of f 1 (). Then, identif the transformation on f() and the effect on the inverse. 5. h() 5 f() h 1 () 5 f 1 ( ) ( 1 1, ) ( 1, 1 ) (, ) (, ) (1, ) (, 1) Transformation on f(): vertical dilation of Effect on the inverse: horizontal dilation of Chapter 1 Skills Practice 1

36 Lesson 1.5 Skills Practice page. m() 5 1 f() m1 () 5 Transformation on f(): 1 Effect on the inverse: 7. h() 5 f() h 1 () 5 Transformation on f(): Effect on the inverse:. h() 5 f ( ) h1 () 5 Transformation on f(): Effect on the inverse: Chapter 1 Skills Practice

37 Lesson 1.5 Skills Practice page 9 Name Date 9. h() 5 1f() h 1 () 5 Transformation on f(): 1 Effect on the inverse: 3. h() 5 f(1) h 1 () 5 Transformation on f(): Effect on the inverse: Chapter 1 Skills Practice 3

38 Lesson 1.5 Skills Practice page 1 Given each function f(), write an equation for the inverse function f 1 (). 31. f() f() 5? 3 f 1 () log () f 1 () f() 5 log 5 ( 3 ) 3. f() 5 1 log () f 1 () 5 f 1 () f() 5 log() 3. f() 5? 5 f 1 () 5 f 1 () 5 Chapter 1 Skills Practice