Describe each type of account as simple interest or compound interest based on the scenario given. Explain your reasoning.

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1 Lesson.1 Skills Practice Name Date Go for the Curve! Comparing Linear and Eponential Functions Vocabular Describe each tpe of account as simple interest or compound interest based on the scenario given. Eplain our reasoning. 1. Andrew deposits $300 into an account that earns % interest each ear. After the first ear, Andrew has $30 in the account. After the second ear, Andrew has $31 in the account, and after the third ear, Andrew has $31 in the account.. Mariln deposits $00 in an account that earns 1.% interest each ear. After the first ear, Mariln has $09 in the account. After the second ear, Mariln has $1.1 in the account, and after the third ear, Mariln has $7.1 in the account. Problem Set 01 Carnegie Learning Write a function to represent each problem situation. 1. Nami deposits $00 into a simple interest account. The interest rate for the account is 3%. Write a function that represents the balance in the account as a function of time t. P(t) P 0 1 (P 0? r)t P(t) 00 1 (00? 0.03)t P(t) t. Carmen deposits $1000 into a simple interest account. The interest rate for the account is %. Write a function that represents the balance in the account as a function of time t. Chapter Skills Practice 31

2 Lesson.1 Skills Practice page 3. Emilio deposits $0 into a simple interest account. The interest rate for the account is.%. Write a function that represents the balance in the account as a function of time t.. Vance deposits $100 into a simple interest account. The interest rate for the account is.%. Write a function that represents the balance in the account as a function of time t.. Perr deposits $17 into a simple interest account. The interest rate for the account is.%. Write a function that represents the balance in the account as a function of time t.. Julian deposits $000 into a simple interest account. The interest rate for the account is.7%. Write a function that represents the balance in the account as a function of time t. Sherwin deposits $00 into a simple interest account. The interest rate for the account is 3.7%. The function P(t) t represents the balance in the account as a function of time. Determine the account balance after each given number of ears ears. ears P(t) t P(3) (3) P(3). In 3 ears, the account balance will be $ ears ears 01 Carnegie Learning 3 Chapter Skills Practice

3 Lesson.1 Skills Practice page 3 Name Date ears 1. 7 ears Hector deposits $00 into a simple interest account. The interest rate for the account is.%. The function P(t) t represents the balance in the account as a function of time. Determine the number of ears it will take for the account balance to reach each given amount. 13. $0 1. $10 P(t) t t 10 1t t It will take ears for the account balance to reach $0. 1. $10 1. $00 01 Carnegie Learning 17. double the original deposit 1. triple the original deposit Chapter Skills Practice 33

4 Lesson.1 Skills Practice page Write a function to represent each problem situation. 19. Ronna deposits $00 into a compound interest account. The interest rate for the account is %. P(t) P 0? (1 1 r) t P(t) 00? ( ) t P(t) 00? Leon deposits $0 into a compound interest account. The interest rate for the account is %. 1. Chen deposits $100 into a compound interest account. The interest rate for the account is 3.%.. Serena deposits $700 into a compound interest account. The interest rate for the account is.%. 3. Shen deposits $300 into a compound interest account. The interest rate for the account is 1.7%.. Lea deposits $0 into a compound interest account. The interest rate for the account is.%. 01 Carnegie Learning 3 Chapter Skills Practice

5 Lesson.1 Skills Practice page Name Date Cisco deposits $00 into a compound interest account. The interest rate for the account is 3.%. The function P(t) 00? 1.03 t represents the balance in the account as a function of time. Determine the account balance after each given number of ears.. ears. ears P(t) 00? 1.03 t P() 00? 1.03 P() In ears, the account balance will be $ ears. 0 ears 9. 0 ears 30. ears 01 Carnegie Learning Mario deposits $1000 into a compound interest account. The interest rate for the account is %. The function P(t) 1000? 1.0 t represents the balance in the account as a function of time. Use a graphing calculator to estimate the number of ears it will take for the account balance to reach each given amount. 31. $ $000 It will take about.3 ears for the account balance to reach $ $ $10,000 Chapter Skills Practice 3

6 Lesson.1 Skills Practice page 3. double the original amount 3. triple the original amount Use the simple and compound interest formula to complete each table. Round to the nearest cent. 37. Teresa has $300 to deposit into an account. The interest rate available for the account is %. Quantit Time Simple Interest Balance Compound Interest Balance Units ears dollars dollars Epression t t 300? 1.0 t Ye has $700 to deposit into an account. The interest rate available for the account is %. Quantit Time Simple Interest Balance Compound Interest Balance Units Epression Carnegie Learning 0 3 Chapter Skills Practice

7 Lesson.1 Skills Practice page 7 Name Date 39. Pablo has $1100 to deposit into an account. The interest rate available for the account is 3.%. Quantit Time Simple Interest Balance Compound Interest Balance Units Epression T has $ to deposit into an account. The interest rate available for the account is.%. Quantit Time Simple Interest Balance Compound Interest Balance Units Epression 0 01 Carnegie Learning Chapter Skills Practice 37

8 Lesson.1 Skills Practice page 1. Xavier has $300 to deposit into an account. The interest rate available for the account is 3.7%. Quantit Time Simple Interest Balance Compound Interest Balance Units Epression 0 1. Denisa has $100 to deposit into an account. The interest rate available for the account is.%. Quantit Time Simple Interest Balance Compound Interest Balance Units Epression Carnegie Learning 3 Chapter Skills Practice

9 Lesson. Skills Practice Name Date Downtown and Uptown Graphs of Eponential Functions Vocabular Define the term in our own words. 1. horizontal asmptote Problem Set Write a function that represents each population as a function of time. 1. Blueville has a population of Its population is increasing at a rate of 1.%. P(t) P 0? (1 1 r) t P(t) 7000? ( ) t P(t) 7000? 1.01 t. Youngstown has a population of 1,000. Its population is increasing at a rate of 1.%. 3. Greenville has a population of 000. Its population is decreasing at a rate of 1.7%. 01 Carnegie Learning. North Park has a population of 1,000. Its population is decreasing at a rate of 3.1%. Chapter Skills Practice 39

10 Lesson. Skills Practice page. West Lake has a population of 900. Its population is increasing at a rate of.%.. Springfield has a population of 11,00. Its population is decreasing at a rate of 1.%. Wanesburg has a population of 1,000. Its population is increasing at a rate of 1.%. The function P(t) 1,000? 1.01 t represents the population as a function of time. Determine the population after each given number of ears. Round our answer to the nearest whole number ear. 3 ears P(t) 1,000? 1.01 t P(1) 1,000? P(1) 1,0 The population after 1 ear will be 1,0. 9. ears ears ears 1. 0 ears 01 Carnegie Learning 370 Chapter Skills Practice

11 Lesson. Skills Practice page 3 Name Date Morristown has a population of 1,000. Its population is decreasing at a rate of 1.%. The function, P(t) 1,000? 0.9 t represents the population as a function of time. Use a graphing calculator to estimate the number of ears it will take for the population to reach each given amount , ,000 It will take about.7 ears for the population to reach 17, half 1. one-third ,000 Complete each table and graph the function. Identif the -intercept, -intercept, asmptote, domain, range, and interval(s) of increase or decrease for the function. 19. f() 01 Carnegie Learning f() intercept: none intercept: (0, 1) asmptote: 0 domain: all real numbers range:. 0 interval(s) of increase or decrease: increasing over the entire domain Chapter Skills Practice 371

12 Lesson. Skills Practice page 0. f() f() f() 1 3 f() Carnegie Learning 37 Chapter Skills Practice

13 Lesson. Skills Practice page Name Date. f() 1 f() f()? f() 01 Carnegie Learning Chapter Skills Practice 373

14 Lesson. Skills Practice page. f()? 1 f() Carnegie Learning 37 Chapter Skills Practice

15 Lesson.3 Skills Practice Name Date Let the Transformations Begin! Translations of Linear and Eponential Functions Vocabular Match each definition to its corresponding term. 1. the mapping, or movement, of all the points of a figure in a plane according to a common operation A basic function. a tpe of transformation that shifts the entire graph left or right B transformation 3. a function that can be described as the simplest function of its tpe C vertical translation. a tpe of transformation that shifts the entire graph up or down D coordinate notation. the variable on which a function operates E argument of a function. notation that uses ordered pairs to describe a transformation on a coordinate plane Problem Set F horizontal translation 01 Carnegie Learning Rewrite each function g() in terms of the basic function f(). 1. f(). f() g() 1 g() 7 g() f() 1 3. f(). f() 3 g() g() f() 3. f() g() 3 1 g() Chapter Skills Practice 37

16 Lesson.3 Skills Practice page Represent each vertical translation, g(), using coordinate notation. 7. f(). f() g() 1 g() 1 9 (, ) (, 1 ) 9. f() 10. f() g() g() f() 1. f() 3 g() 1 g() 3 Rewrite each function g() in terms of the basic function f(). 13. f() 3 1. f() 3 g() 3 ( 1 1) ( 1 ) g() 3 g() 3 ( 1 1) f( 1 1) 1. f() 1. f() g() ( 1) ( 9) g() 17. f() 1. f() g() ( 3) g() ( 1 ) Represent each horizontal translation, g(), using coordinate notation. 19. f() 3 0. f() 3 g() 3 ( ) ( 1 ) g() 3 (, ) ( 1, ) 1. f(). f() g() ( 1 1) ( 3) g() 01 Carnegie Learning 3. f() 3. f() 3 g() 3( 1) g() 3( 1 1) 37 Chapter Skills Practice

17 Lesson.3 Skills Practice page 3 Name Date Describe each graph in relation to its basic function.. Compare f() () 1 b when b, 0 to the basic function h(). The graph of f() is b units below the graph of h().. Compare f() b c when c. 0 to the basic function h() b. 7. Compare f() ( b) when b. 0 to the basic function h().. Compare f() b c when c, 0 to the basic function h() b. 9. Compare f() b 1 k when k. 0 to the basic function h() b. 30. Compare f() ( b) when b, 0 to the basic function h(). Each coordinate plane shows the graph of f(). Sketch the graph of g(). 31. g() f() 1 3. g() f() 1 01 Carnegie Learning Chapter Skills Practice 377

18 Lesson.3 Skills Practice page 33. g() f() 3. g() f( 3) g() f( 1 3) 3. g() f( ) g() f() 1 3. g() f( 1 ) Carnegie Learning 37 Chapter Skills Practice

19 Lesson.3 Skills Practice page Name Date Write the equation of the function given each translation. 39. f() 0. f() Vertical translation up units Vertical translation down units g() 1 1. f() 3. f() Horizontal translation right units Horizontal translation left units 3. f() 3. f() Vertical translation down units Horizontal translation right 3 units Each graph shows the function g() as a translation of the function f(). Write the equation of g() Carnegie Learning g() 3 Chapter Skills Practice 379

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21 Lesson. Skills Practice Name Date Take Some Time to Reflect Reflections of Linear and Eponential Functions Vocabular Define each term in our own words. 1. reflection. line of reflection Problem Set Rewrite each function g() in terms of the basic function f(). 1. f() 3 g() ( 3 ) g() f(). f() 3 g() 3 3. f() g() ( ). f() g() 01 Carnegie Learning. f() 1 g() 1. f() 1 g() ( 1) Chapter Skills Practice 31

22 Lesson. Skills Practice page Represent each reflection using coordinate notation. Identif whether g() is a reflection about a horizontal line of reflection or a vertical line of reflection. 7. f() g() ( ) (, ) (, ) g() is a horizontal reflection about 0.. f() g() 9. f() g() () 10. f() g() () 11. f() g() f() 3 g() ( 3) Each coordinate plane shows the graph of f(). Sketch the graph of g(). 13. g() f() 1. g() f() Carnegie Learning 3 Chapter Skills Practice

23 Lesson. Skills Practice page 3 Name Date 1. g() f() 1. g() f() g() f() 1. g() f() Carnegie Learning Chapter Skills Practice 33

24 Lesson. Skills Practice page Write a function, g(), to describe each reflection of f(). 19. f() 3 Reflection about the horizontal line 0. g() 3 0. f() Reflection about the vertical line f() 1 Reflection about the vertical line 0.. f() 7 Reflection about the horizontal line f() 1 9 Reflection about the horizontal line 0.. f() 1 1 Reflection about the vertical line 0. Write an equation for g() given each transformation. Sketch the graph of g().. f() g() is a reflection of f() over the line 0. g(). f() g() is a reflection of f() over the line Carnegie Learning 3 Chapter Skills Practice

25 Lesson. Skills Practice page Name Date 7. f() 3 g() is a translation of f() up units.. f() g() is a translation of f() right 3 units f() g() is a translation of f() down units. 30. f() 3 g() is a translation of f() left units. 01 Carnegie Learning 0 0 Chapter Skills Practice 3

26 Lesson. Skills Practice page Identif the transformation required to transform f() to g() as shown in each graph g() is a reflection of f() over the line Carnegie Learning 3 Chapter Skills Practice

27 Lesson. Skills Practice page 7 Name Date Identif the transformation required to transform each f() to g(). 37. f() g() ( ) g() is a reflection of f() over the line f() 9 g() f() g() 0. f() 3 g() Carnegie Learning 1. f() 10 g() f() 1 g() 1( 1 1) Chapter Skills Practice 37

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29 Lesson. Skills Practice Name Date Radical! Because It s Cliché! Properties of Rational Eponents Vocabular Match each definition to its corresponding term. 1. the number a in the epression n a A cube root. the number b when b 3 a B inde 3. the eponent n 1 1 in the epression a n C nth root. the number n in the epression n a D radicand. the number b when b n a E rational eponent 01 Carnegie Learning Problem Set Write each epression as a single power Chapter Skills Practice 39

30 Lesson. Skills Practice page Evaluate each epression Evaluate each epression Write each radical as a power Carnegie Learning 3.. z 390 Chapter Skills Practice

31 Lesson. Skills Practice page 3 Name Date Write each power as a radical a 1 9. d c 1 Write each epression in radical form m 01 Carnegie Learning Chapter Skills Practice 391

32 Lesson. Skills Practice page Write each epression in rational eponent form n 1. p 7. m 3 01 Carnegie Learning 39 Chapter Skills Practice

33 Lesson. Skills Practice Name Date Checkmate! Solving Eponential Functions Problem Set Complete each table. Write a function that represents the data in the table and eplain how ou determined our epression. 1.. f() Epression f() Epression The eponents of the epressions in the third column equal. So, f() Carnegie Learning Chapter Skills Practice 393

34 Lesson. Skills Practice page 3.. f() Epression f() Epression f() Epression f() Epression Carnegie Learning 39 Chapter Skills Practice

35 Lesson. Skills Practice page 3 Name Date Graph each function. 7. f() 3. f() f()? 10. f()? Carnegie Learning Chapter Skills Practice 39

36 Lesson. Skills Practice page 11. f() 1. f() Use the intersection feature of our graphing calculator to answer each question. 13. For the function f() 1 determine the value of for which f() 777. For the function f() 1, f() 777 when. 1. For the function f() 1 determine the value of for which f() For the function f() 11 determine the value of for which f(). 1. For the function f() 1 determine the values of for which f(), For the function f() 3 11 determine the values of for which f() For the function f() 1 determine the values of for which f() 1,. 01 Carnegie Learning 39 Chapter Skills Practice

37 Lesson. Skills Practice page Name Date Solve each eponential equation for Carnegie Learning Chapter Skills Practice 397

38 Lesson. Skills Practice page For each pair of epressions, determine whether the second epression is an equivalent form of the first epression. 7. s1 1 () 1? s s (3) () (10) 31. () ( 1 ) 31 Write the eponential function represented b the table of values f() a? b f()? b 1? b 1 1 b f() ( 1 ) Carnegie Learning 39 Chapter Skills Practice

39 Lesson. Skills Practice page 7 Name Date Carnegie Learning Chapter Skills Practice 399

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