Small Investment, Big Reward
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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 A geometric sequence written in function notation. It gets its name because the variable is in the eponent.. half-life The amount of time it takes a substance to deca to half of its original amount. 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? ? ? 19,3 5 9, a n 5? (.5) n1 a 1 5 (.5) 11 5 (.5) 9 < (.1953) < Chapter 1 Skills Practice 97
2 Lesson 1.1 Skills Practice page a n 5 1? 1.5 n1 a 1 5 1? ? < a n 5 1?. n1 a 1 5 1? ?. 9 < a n 5.? n1 a 1 5.? ? 9 5.? a n 5 7? ( 1 3 ) n1 a ( 1 3 ) ( 1 3 ) 9 < 7(.5) < Chapter 1 Skills Practice
3 Lesson 1.1 Skills Practice page 3 Name Date Write an eponential function 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 < 1.? < 15,5.79. a n 5.3? n1 n 5 3 f(n) 5.3? n1 5.3? n? 1 5.3? n? ? n f(3) 5.375? ? a n 5 15?. n1 n 5 f(n) 5 15?. n1 5 15?. n? ?. n? ?. n f() ? ? a n 5.5? 1.5 n1 n 5 f(n) 5.5? 1.5 n1 5.5? 1.5 n? ? 1.5 n? ? 1.5 n f() 5.? 1.5 <.? <.73 1 Chapter 1 Skills Practice 99
4 Lesson 1.1 Skills Practice page 11. a n 5 1? n1 n 5 7 f(n) 5 1? n1 5 1? n? 1 5 1? n? 1 5.5? n f(7) 5.5? 7 5.5? 1,3 5,9 1. a n 5 1,?.5 n1 n 5 5 f(n) 5 1?.5 n1 5 1?.5 n? ?.5 n? 5?.5 n f(5) 5?.5 5 5? 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 < 1(.9) < Elapsed Time (minutes) Bacteria Subject to Growth Inhibitor Number of Half-Life Ccles 1 3 A(t) 5 ( 1 A(1) 5 ( 1 t ) 5 1 ) 5 5 ( 1 ) < (.95) <.73 7 Chapter 1 Skills Practice
5 Lesson 1.1 Skills Practice page 5 Name Date 15. Elapsed Time (ears) Strontium in Rock Sample (grams) Number of Half-Life Ccles t ) 1 ) 3 ) A(t) 5 1 ( 1 A(1) 5 1 ( ( < 1(.35) < Elapsed Time (ears) 5,7 11, 15,75 17,1, C-1 in Rock Sample (grams) Number of Half-Life Ccles A(t) 5 1 ( 1 A(15,75) 5 1 ( ( 1 t ) 5,7 15,75 ) 11 ) 5,7 < 1(.17) <.17 1 Chapter 1 Skills Practice 71
6 Lesson 1.1 Skills Practice page 17. Elapsed Time (Das) 1 1 Rat Population Eposed to Virus Number of Half-Life Ccles A(t) 5 5, ( 1 A() 5 5, ( 1 t ) ) 5 5, ( 1 ) 7 < 5,(.7) < Elapsed Time (Hours) 1 Participants in Tennis Tournament Number of Half-Life Ccles 1 3 A(t) 5 5 ( 1 A(1) 5 5 ( 1 t ) 1 ) 5 5 ( 1 ) < 5(.39) 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. Both are smbols that represent irrational numbers and are constants that are used to simplif calculations. The natural base e represents continuous growth and is used to model population changes, radioactive deca of a substance, and other phsics and calculus applications. It is approimatel equal to.71. The number p represents the ratio of a circle s circumference to its diameter and is used in man geometr formulas for area and volume of geometric shapes. It is approimatel equal to Problem Set Identif each function as eponential growth or deca. Eplain our reasoning. 1. f() 5. f() 5. The function represents eponential The function represents eponential deca growth because the base is greater than 1. because the base is between and f() 5 ( 5 ). f() 5 5 The function represents eponential The function represents eponential growth growth because the base is greater than 1. because the base is greater than f() 5 ( 1 ). f() The function represents eponential deca The function represents eponential growth because the base is between and 1. because the base is greater than 1. Chapter 1 Skills Practice 73
8 Lesson 1. Skills Practice page Complete each table and graph the eponential function. 7. f() 5 f() f() 5 ( 1 ) 1 f() Chapter 1 Skills Practice
9 Lesson 1. Skills Practice page 3 Name Date 9. f() f() f() 5 ( 5 ) 1 f() Chapter 1 Skills Practice 75
10 Lesson 1. Skills Practice page 11. f() 5 f() f() 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. Answers will var. f() 5 9 f() 5 ( 3 ) as `, f() 15. end behavior: as `, f() ` 1. decreasing over (`, `) reference point (,.5) reference point (, 1) Answers will var. f() f() 5 ( 1 Answers will var. ) as `, f() ` 17. increasing over (`, `) 1. end behavior: as `, f() reference point ( 3, 1 ) reference point (, 1 Answers will var. f() 5 f() 5 ( Answers will var. 3 ) 1 ) 1 Chapter 1 Skills Practice 77
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. 19. An investor deposits $1, in an account that promises 5% interest calculated 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 3.5% compound interest at the end of a ear. If $5 is collected in PTA dues, how much mone will the school have at the start of the net school ear? The school will have $,57.5 at the start of the net school ear. A(t) 5 P ( r 1 1 n ) n? t A(1) 5,5 ( ? 1 ) 1 5,5(1.35) 1 5, Kle put $3 of his birthda mone in the bank. The bank compounds interest twice a ear at %. How much mone will Kle have after three ears? Kle will have $337.5 after three ears. A(t) 5 P ( r 1 1 n ) n? t A(3) 5 3 ( 1 1.? 3 ) 5 3(1.) < 3(1.1) < 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 compounds interest monthl at a rate %. How much mone will the group have at the end of 1 ears? The group will have $9,99. at the end of 1 ears. A(t) 5 P ( 1 1 r n ) n? t A(1) 5 5, ( ? 1 ) 1 5 5,(1.5) 1 < 5,(1.) < 9, Interest is compounded quarterl at Mone Bank at a 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? There will be $9,99. in the account after si ears. A(t) 5 P ( r 1 1 n ) n? t A() 5 7, ( ? ) 5 7,(1.1375) < 7,(1.37) < 9,99.. 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.% and another bank that compounds interest monthl at.%. Which bank will earn her more mone? She earns $5. from the first bank and $5. from the second bank. The bank that compounds interest monthl with a.% interest rate will earn Sasha more mone. A(t) 5 P ( 1 1 r n ) n? t A(.5) 5 5 ( ).5? 35 < 5 (1.) 9 < 5(1.55) < 5. A(t) 5 P ( 1 1 r n ) n? t A(.5) 5 5 ( ).5? 1 5 5(1. ) 3 < 5(1.1) < 5. 1 Chapter 1 Skills Practice 79
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 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. The population of Boston, Massachusetts is growing at a rate of 1.%. The population in 13 was approimatel 3,5. What is the predicted population for 5? The predicted population of Boston, Massachusetts for 5 is 79,9. N(t) 5 N o e rt N(1) 5 3,5e (.1? 1) 5 3,5 e.1 < 79, The population of Charlotte, North Carolina in 13 was approimatel 775,. If the rate of growth is about 3.%, what is an approimation of Charlotte s population in? In, the population of Charlotte, North Carolina was approimatel 511,5 people. N(t) 5 N o e rt N(13) 5 775, e (.3? 13) 5 775,e.1 < 511,5 71 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 a rate of about 5.5%. What is an approimation of Beijing s population in 19? In 19, the population of Beijing, China was approimatel 3,559,. N(t) 5 N o e rt N(3) 5,9,e (.55? 3) 5,9,e 1.7 < 3,559, 9. The population of Detroit, Michigan is decreasing at a rate of about.75%. Detroit s population in 13 was approimatel 7,. What is the predicted population for 15? The predicted population for Detroit, Michigan in 15 is 9,57. N(t) 5 N o e rt N() 5 7, e (.75? ) 5 7, e.15 < 9, The population of Berlin, German was about 3,9, in 11. Its population is declining at a rate of about.%. What is the predicted population for 5? In 5, the population for Berlin, German will be about 3,3,133 people. N(t) 5 N o e rt N(39) 5 3,9, e (.? 39) 5 3,9, e.7 < 3,3,133 Chapter 1 Skills Practice 711
16 1 71 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, ) (, ) Domain: All real numbers Range:.. Horizontal asmptote: 5 f() 5 c() 5 f() 1 Reference Points on f() Corresponding Points on c() ( 1, 1 ) ( 1, 7 ) (, 1) (, 1) (1, ) (1, ) f() c() Domain: All real numbers Range:. Horizontal asmptote: 5 Chapter 1 Skills Practice 713
18 Lesson 1.3 Skills Practice page 3. f() 5 3 c() 5 f(3) Reference Points on f() Corresponding Points on c() ( 1, 1 3 ) ( 1, ) c() f() (, 1) (, 1) (1, 3) ( 1 3, 3 ) Domain: All real numbers Range:. Horizontal asmptote: 5. f() 5 c() 5 f() 1 Reference Points on f() Corresponding Points on c() ( 1, 1 ) (1, ) c() (, 1) (, ) f() (1, ) (1, ) Domain: All real numbers Range:. Horizontal asmptote: 5 71 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() Corresponding Points on c() ( 1, 1 5 ) (, 1 5 ) c() (, 1) (3, 1) f() (1, 5) (, 5) Domain: All real numbers Range:. Horizontal asmptote: 5. f() 5 c() 5 f() 1 Reference Points on f() Corresponding Points on c() ( 1, 1 ) ( 1, 1 ) (, 1) (, 3) c() f() 1 (1, ) (1, ) Domain: All real numbers Range:. Horizontal asmptote: 5 Chapter 1 Skills Practice 715
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) 5 ( 1, ) (, ) (1, 5) 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) (1, ) (, ) ( 3, 1) 1 (, ) To create g(), the graph of f() is reflected over the -ais and horizontall translated right 3 units. g() 5 f(3 ) 71 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() To create g(), the graph of f() was reflected over the -ais and verticall translated up 3 units. g() 5 f() f() g() 1 ( 1, ) 3 (1, 3) (, 1) ( 1, 3) (, 1) 1 (, 3 ) 3 To create g(), the graph of f() was horizontall translated left 1 unit and verticall translated down units. g() 5 f( 1 1) Chapter 1 Skills Practice 717
22 Lesson 1.3 Skills Practice page 11. f() 1 g() (1, ) ( 1, ) (, 1) 1 1 (, ) 3 (, ) To create g(), the graph of 1 f() was stretched verticall b a factor of and compressed horizontall b a factor of 3. g() 5 f(3) 1. f() g() ( 1, 1) 1 1 ( 1, ) 5 (, 1) (1, 5) (, ) 1 (1, 5 ) 5 To create g(), the graph of f() was reflected over the -ais and verticall translated up 5 units. g() 5 f() 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() The graph of the function m() is stretched verticall b a factor of 3 and verticall translated down units to produce t(). t() 5 3? e m() t() 5 1 m() 1 1 The graph of the function m() is compressed verticall b a factor of and verticall translated up units 1 to produce t(). t() 5? e m() 5 t() 5 m(3 1) The graph of the 1 1 function m() is compressed horizontall b a factor of and horizontall 3 translated right units to produce t(). 3 t() 5 31 Chapter 1 Skills Practice 719
24 Lesson 1.3 Skills Practice page 17. m() 5 7 t() 5 m(.5 1 ) The graph of the function m() is stretched horizontall b a factor of and horizontall translated left units to produce t(). t() m() 5 t() 5 m() 1 3 The graph of the function m() is reflected over the -ais and reflected over the -ais, stretched verticall b a factor of, and verticall translated up 3 units to produce t(). t() 5? 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 logarithm of a number for a given base is the eponent to which the base must be raised in order to produce that number.. A natural logarithm is a logarithm with base e, and is usuall written as ln. 3. A logarithmic function is a function involving a logarithm.. A common logarithm 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 log 5 (5) , log ( 1 ) 5 3 log ( 1 1, ) ( 1 ) ( 1 11 ) 5 11 log 1 ( 1 3 ) 5 5 log 5 1 (11) 11 Chapter 1 Skills Practice 71
26 Lesson 1. Skills Practice page Write each logarithmic equation as a corresponding eponential equation. 7. log 7 ( 1 9 ) 5. log ( 1 ( ) 5 3 ) log (1) log ( 1 19 ) log 1 ( ) log (79) ( 1 5 ) 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() 1 f 1 () f 1 () Domain:. Domain:. Range: All real numbers Range: All real numbers Asmptotes: 5 Asmptotes: 5 End behavior: As, `. End behavior: As,. As 1`, 1`. As 1, 1. 7 Chapter 1 Skills Practice
27 Lesson 1. Skills Practice page 3 Name Date 15. f() f() 5 f() f() f 1 () f 1 () Domain:. Domain:. Range: All real numbers Range: All real numbers Asmptotes: 5 Asmptotes: 5 End behavior: As,. End behavior: As,. As 1, 1. As 1, 1. 1 Chapter 1 Skills Practice 73
28 Lesson 1. Skills Practice page 17. f() 5 e 1. f() 5 5 f() f() f 1 () f 1 () Domain:. Domain:. Range: All real numbers Range: All real numbers Asmptotes: 5 Asmptotes: 5 End behavior: As,. End behavior: As,. As 1, 1. As 1, 1. 1 Solve each logarithmic equation log 9 ( 1 b )..93 <? log (.5) 1 1 b ? b b log (3)..39 < log b n n ( 1 ) b n b n < ln z log ( g 1 ) e.5 z? (1.39) 5 log ( g 1 ) 1. z.9 5 log ( g 1 ) g 1 g. 1 g 7 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() f() = log () f() = log 3 () g() The graph of g() was horizontall translated The graph of g() was verticall translated right units to produce the graph of g(). up 3 units to produce the graph of g(). g() 5 log ( ) g() 5 log 3 () Chapter 1 Skills Practice 75
30 Lesson 1.5 Skills Practice page 3.. g() f() = log () f() = log 5 () g() The graph of g() was horizontall translated left units and verticall translated down 5 units to produce the graph of g(). g() 5 log ( 1 ) 5 The graph of g() was stretched verticall b a factor of to produce the graph of g(). g() 5 log 5 () 1 5. g() f() = log (). g() f() = log () The graph of g() was reflected over the The graph of g() was reflected over the -ais -ais and horizontall translated right and horizontall translated up 3 units to 3 units to produce the graph of g(). produce the graph of g(). g() 5 log ( 3) g() 5 log ( 1 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(): (`, `) m() 5 f() 1 f() 5 log() Asmptote of m(): 5. m() 5 f( ). Domain of m(): (, `) 1 Range of m(): (`, `) f() 5 log() Asmptote of m(): 5 m() 5 f( ) Chapter 1 Skills Practice 77
32 Lesson 1.5 Skills Practice page 9. m() 5 f( 1 1) 3. Domain of m(): (1, `) Range of m(): (`, `) f() 5 log() Asmptote of m(): 5 1 m() 5 f( 1 1) 3 1. m() 5 f( 3). Domain of m(): ( 3, ` ) 1 Range of m(): (`, `) f() 5 log() Asmptote of m(): 5 3 m() 5 f( 3) 7 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(): (`, `) m() 5.5f()11 f() 5 log() Asmptote of m(): 5 1. m() 5 f( ) 1 Domain of m(): (, `) m() 5 f( ) 1 1 Range of m(): (`, `) Asmptote of m(): 5 f() 5 log() Chapter 1 Skills Practice 79
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. Answers will var. c() 5 f ( ) c() 5 f( 1 3) 15. Reference Points on f() Corresponding Points on c() 1, 1 ( 1, 3 ) (1, ) (1, ) 1. vertical asmptote at 5 Answers will var. c() 5 f( 1 ) (, 1) (, 3) c() 5 3f() domain: (, `) 1. point: (5, ) Answers will var. c() 5 f( ) Reference Points on f() Corresponding Points on g() ( 1, 1 ) ( 1, 3 ) (1, ) (1, ) (, 1) (, 1) c() 5 f() 1 73 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) g 1 () 5 f 1 () 1 1. g() 5 f( 1 ). g() 5 f() 5 g 1 () 5 f 1 () g 1 () 5 f 1 ( 1 5) 3. g() 5 f( 1 1) 3. g() 5 f( ) 1 g 1 () 5 f 1 ( 1 3) 1 g 1 () 5 f 1 ( ) 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, ) (, 1) Transformation on f(): vertical dilation of Effect on the inverse: horizontal dilation of Chapter 1 Skills Practice 731
36 Lesson 1.5 Skills Practice page. 1 m() 5 f() m 1 () 5 f 1 ( ) ( 1, 1 1 ) ( 1 1, 1 ) ( 1, ) ( 1, ) (1, 1) (1, 1) Transformation on f(): vertical dilation of 1 Effect on the inverse: horizontal dilation of 1 7. h() 5 f() ( 1, 1 1 h 1 () 5 f 1 () 1, ) ) ( 1 1 (, 1) (1, ) ( 1, ) (, 1 ) Transformation on f(): horizontal dilation of 1 Effect on the inverse: vertical dilation of 1. h() 5 f ( ) h 1 () 5 f 1 () (, 1 ) ( 1, ) (, 1) (1, ) (, ) (, ) Transformation on f(): horizontal dilation of Effect on the inverse: vertical dilation of 73 Chapter 1 Skills Practice
37 Lesson 1.5 Skills Practice page 9 Name Date 9. h() 5 1f() h 1 () 5 f 1 ( 1 ) (1, 3) (3, 1) (, 1) (1, ) (1, ) (, 1) Transformation on f(): vertical dilation of 1 Effect on the inverse: horizontal dilation of 1 3. h() 5 f(1) h 1 () f 1 (), 1 ) ( 1 ( 1 1, 1 1 ) (, 1) (1, ) ( 1 1, ) (, 1 1 ) 1 Transformation on f(): horizontal dilation of 1 Effect on the inverse: vertical dilation of 1 Chapter 1 Skills Practice 733
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 () 5 log 3 ( ) 33. f() 5 log 5 ( 3 ) 3. f() 5 1 log () f 1 () 5 3? 5 f 1 () f() 5 log() 3. f() 5? 5 f 1 () 5 1 f 1 () log ( ) 73 Chapter 1 Skills Practice
Small Investment, Big Reward
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
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