Unit 5 Homework

Exponential &

Logarithmic Functions

1

Honors Algebra 2 WS#1 Name __________________________

Unit 5 – Worksheet #1

Applications:

1. An acidophilus culture containing 150 bacteria doubles in population every hour.

a. Write a function representing the bacteria population for every hour that passes.

b. Predict the number of bacteria present after 12 hours.

2. A new softball dropped onto a hard surface from a height of 25 inches rebounds to about 25

the

height on each successive bounce.

a. Write a function representing the rebound height for each bounce.

b. After how many bounces would a new softball rebound less than one inch?

3. A quantity of insulin used to regulate sugar in the bloodstream breaks down by 5% each minute. A

body-weight adjusted initial dose is generally 10 units.

a. Write a function representing the amount of the dose that remains.

b. How much insulin remains after 10 minutes?

4. The Dutch purchased Manhattan Island in 1626 for $24 worth of merchandise. Suppose that

instead, $24 had been invested at that time in an account that paid 3.5% interest each year. Find

the balance in 2008.

5. If a computer valued at $2765 depreciates at a rate of 30% per year.

a. How much will the computer be worth in 2 years?

b. Estimate the number of years it will take for the computer’s value to be less than $350.

2

6. The compound interest formula is 1

ntr

A Pn

= +

. Harry invested $5000 at 5% interest compounded

quarterly.

a. How much will the investment be worth after 5 years?

b. When will the investment be worth more than $10,000?

c. If Harry could have invested the same amount in an account that paid 5% interest

compounded monthly, how much more would his investment have been worth after 5 years?

7. Aidan has $7565 in his checking account. He invests $5000 of it in an account that earns 3.5%

interest compounded continuously. What is the total amount of his investment after 3 years?

9. If you deposit $5000 in an account that pays 6% annual interest, how much would you have in

the account after one year if the interest were compounded…

a) annually

b) semiannually

c) quarterly

d) monthly

e) continuously

10. Which function grows faster as x increases, 3x or 3x ? Is there a time that these two functions will

be equal? Explain (in words) your reasoning.

3

Honors Algebra 2 Name __________________________

Unit 1 – Worksheet #2

Graph the function. State the domain, range, and end behavior and asymptote. Circle Growth or Decay or Neither.

1. y = 3x - 2 2. f(x) = (1/2)x + 3 3. y = 1

2· 2x

Intercepts_______________ EB _____________________ Intercepts ______________

Growth Decay Neither Growth Decay Neither Growth Decay Neither

Asymptote_____________ Asymptote_____________ Asymptote_____________

4. y = - 2x + 4 5. f(x) = 2 (3)x 6. f(x) = 2x-4 - 3

Domain ________________ Domain ________________ Domain ________________

Range _________________ Range _________________ Range _________________

EB _____________________ EB _____________________ EB _____________________

Growth Decay Neither Growth Decay Neither Growth Decay Neither

Asymptote_____________ Asymptote_____________ Asymptote_____________

4

Graph each function, list the characteristics and all transformations from the parent function, y=a(b)x.

13.

21

( ) 2 52

x

f x

+

= − −

14. F(x) = 2(3)x-3 - 5 15.

41

5 62

x

y

−

= −

Domain ________________ Domain ________________ Domain ________________

Range _________________ Range _________________ Range _________________

x-intercept ______________ x-intercept _____________ x-intercept ______________

y-intercept_______________ y-intercept_____________ y-intercept_______________

Growth Decay Neither Growth Decay Neither Growth Decay Neither

Asymptote_____________ Asymptote_____________ Asymptote_____________

Transformations: Transformations: Transformations:

5

MATCH THE FOLLOWING EXPONENTIAL FUNCTIONS WITH THE APPROPRIATE GRAPHS.

16. f(x) = 2x 15. g(x) = 2x – 1 17. h(x) = -2x

18. F(x) = 2-x 19. G(x) = 2x + 1

A) B) C) D) E)

Write the equation of the exponential from the function, y=a(3)x-h + k

20._________________________________________ 21._________________________________________

By hand: Write an exponential model that passes through the given point.

22. (0, 6) and (2, 54) 23. (-1, 27) and (2, 1)

24. (0,16) and (2,1) 25. (2,3) and (4,27)

6

Calculator: Write the exponential model that passes through the given points. Round

answer to the 3rd decimal place.

26. (1, 5.6) (2, 7.8) (3, 12.1) (4, 21.8) 27. (5.1, 16.3) (9.2, 22.9)

28. 29.

7

Honors Algebra 2 Name___________________________

Unit 5 Worksheet #3

Rewrite each equation in exponential form.

1. 4log 64 3= 2.

9

1log 2

81= − 3. 17

log 289 2=

4. 19log 361 2= 5.

15

1log 2

225= − 6.

18

1log 2

324= −

7. log 43 10n

= 8. log 64m

n= 9. log 4y

x = −

10. 1

log19

vn=

Rewrite each equation in logarithmic form.

11. 53 243= 12. 1

2196 14= 13. 2 15

25

− =

14. 1

2144 12= 15. 26 36= 16. 2 17

49

− =

17. 33yx = 18. 17y x= 19. 12uv =

20. 7x y=

21. Fill in the blank: If logb

y x= , then ___________.

8

22. Fill in the table.

Exponential Form Logarithmic Form

72=49

log42=y

xy=z

logx5=3

e4=y

Short answer.

23. What is the base of the common logarithm? 24. What is the base of the natural logarithm?

Evaluate without a calculator.

25. log9 81 26. log8 1 27. log3 1

3 28. log4 2

29. log27 3 30. ln e 31. log7 493 32. 4

1

2

log (0.25)

33. log4 256 34. log41

64 35. log 10 10 36. log4 32

37. log161

2 38. log25 125 39. log2 (0.5)4 40. log2 163

41. log3 3(x+7) 42. 3log34.5

9

Evaluate the logarithms with a calculator. Round all answers to the 3rd decimal place.

43. log21 44. 5log 6 45. ln4.31

46. 4log ( 2)− 47. l ( )5

3n

Use the change of base formula to rewrite.

48. ( )12log 9.7 49. ( )0.45

log 5 50. ( )ln 15

10

Honors Algebra 2 5.4 Name _______________________

Unit 5 Worksheet #4 NO CALCULATORS!

Graph the function. State the domain, range, and the equation of the asymptote.

1. 3

( ) 2log 5f x x= + 2. 4

( ) log ( 2) 1f x x= + − 3. ( )( ) log 8 1f x x= − + −

Domain __________________ Domain __________________ Domain ________________

Range ___________________ Range ___________________ Range _________________

Asymptote _______________ Asymptote _______________ Asymptote _____________

4. 2

1( ) log ( 1) 6

4f x x= + − 5.

4( ) 3log 1f x x= − +

Domain __________________ Domain __________________

Range ___________________ Range ___________________

Asymptote _______________ Asymptote _______________

11

Describe the transformation.

6. from logy x= to ( )9log 1 7y x= − + 7. from 3logy x= to 3

0.5log 5y x= − +

Identify the domain, range, and asymptote.

8. ( )log 5 6y x= − + 9. ( )ln 7y x= −

D:______________ D:____________

R:______________ R:____________

Asy:____________ Asy:__________

10. Write an equation of the graph below given the parent graph is y = log x.

12

Find the inverse of the function.

1. y = log5 x 2. y = ln x 3. 1

5

logy x=

4. y = log 2

x 5. y = log6 (x + 2) 6. y = log3 9x

7. y = 7x 8. y = 3ex + 5 9. y = ln (x + 2)

10. y = log3 4x 11. y = 4x – 3 + 2 12. y = lnx + 4

13. y = 1

2

log (2 ) 3x + 14. y = ln(x – 1) – 3 15. y = log2 8x – 1

13

Honors Algebra 2 5.5 Name _______________________

Unit 5 WS #5 Expanding & Condensing

Match the expression with the logarithm that has the same value.

1. log 2 log 8+ 2. log4 log10− 3. 2log4 log2− 4. 1

3log3

−

A. 2

log5

B. log27 C. log4 D. log8

Expand the expression.

5. 2

7log x y 6.

2

2log

4

x

7. 3log5 x 8. 2

1ln

2x

9.

3

9

2log

3

x 10.

2

6log

xy

z

11. ( )

3

2 2

1log

x

yz

− 12.

3ln x y

13. 2

4log

x

y 14.

2

3

1ln

x

x

−

15. 2 5

9log (2 )x yz 16.

2

6 3

6 9log

3

x x

y

+ +

14

Condense the expression.

17. 3 3 3log 4 log 2 log 2+ + 18. 2ln ln3 ln6x − +

19. 3log log4 log log6x x+ − − 20. 2ln( 1) 2ln ln ln2x y y+ − + +

21. 3 3 3 3log 4 log 5 log 2 log 6+ − − 22. 2log5 2log logx y− +

23. 2 2 2 2

12 log 3 log log 4log

2x y x

+ − −

24. 2ln( 3) ln6 3ln( 2)x x− − − +

25. 3

log( 4) 3log log62

x x+ − − 26. 1

ln3 4ln 2ln( 1)2

x x+ − −

Use log 4 ≈ 0.602 and log 7 ≈ 0.845 to evaluate the logarithm.

27. log 28 28. log 7

4 29. log 16

30. log 70 31. log 1

4 32. log

49

64

15

Honors Algebra 2 5. 6 Name ________________

Unit 5 Worksheet #6 Solving Equations

Solve the exponential equation. Check for extraneous solutions. Round to the nearest thousandths.

1. 5xe = 2. 2 14xe − = 3. 2 5 12xe + =

4. 2 22x = 5. 3 4 6x − = 6. 4 24 54x+ =

7. 2 3 6 13xe − + = 8. 2 32 3 11xe − − = 9. 13 4 8x+ + =

10. ( )6110 5 14

2

x+ − = 11. 3 54 2

2

x− + = 12. 33 1 1xe − =

13. 2 2x xe e− = 14. 2 327 3x x+= 15.

2 1

5 116

2

x

x

−

− =

16. 1

2 24 32x = 17.

2

21

1255

x x−

=

18. 1 43 2x x+ =

16

Solve the logarithmic equation. Check for extraneous solutions. Round the result to the nearest

thousandths place.

1. log(x + 2) = 4 2. 2ln 7 5x − = −

3. 3

log ( 3) 3 5x − + = 4. ln(2 1) ln 0x x− + =

5. 2 2

log log ( 1) 1x x+ + = 6. 3 3

log log ( 8) 2x x+ + =

7. 4 4

1log ( 3) log ( 4)

2x x− + − = 8.

2log(72) log 0

3

x − =

9. log( 5) log( 2)x x− = − 10. 7 7

2log (1 ) log (7 )x x− = −

17

11. ( ) ( )2ln 2 3 ln 9 13x x− = − 12. 3

log log 1 010

x x

+ + + =

13. 2 log3 log12

xx

− =

14. log log

100

xx x

− =

15. 2 2 2

log ( 3) log ( 1) log (6 18)x x x− + + = − 16. 2 2 2

log log ( 4) log ( 2) 4x x x+ + − − =

17. 2 2 2

log (7 8) log ( 1) log ( 1) 1x x x− − + − − = 18. 2

2 2 4log ( 4) log ( 2) log 64x x− − − =

18

Honors Alg 2 5.7 Name _______________________

Unit 5 WS #7 Inequalities/Applications

1. The Consumer Price Index y for a fixed amount of sugar for the year t is given by the equation

87.1ln 171.8y t= − . In how many years did the price of sugar reach $129.60? Round to 2nd decimal

place.

2. Biologists have found that an alligator’s length L (in inches) and weight W (in pounds) can be

related to the function 27.1ln 32.8L W= − where w>4. Find the weight of an alligator that is 84 inches

long. Round to 2nd decimal place.

3. If $2500 is invested in an account where interest is compounded quarterly at 7%, how long before

the investment is doubled? Round to the nearest whole year.

4. A bank compounds interest continuously at 2.4%. How much money was invested initially given

that $5000 is in the account after 15 years? Round to the nearest penny.

5. If the doubling time of a bacteria culture is known to be 3 hours, the population at time t is given

by 3

02t

P P= . If there are 1000 bacteria present now at t=0, & t is measured in hours, find the following:

a. How many bacteria will there be 5 hours from now? Round to nearest whole bacteria

b. When will the population reach 2500? Round to nearest whole hour.

19

Solve the exponential inequality analytically. You must show your number line!

No graphing calculator allowed! Round the nearest thousandths place when necessary.

1. 4 64x 2. 1

164

x

3. 125 5x+ 4. 14 64x+

5. 27 1.5x− 6.

13

102

x+

7. 5 14 0.5x+ 8. 4x-1 + 4 > 12

9. 3ex-2 + 1 ≤ 16 10. 1.4 > -2(3)x

20

Use a graphing calculator to solve. Round to the nearest thousandths place when necessary.

11. 14.5 3 8x+− − − 12. 1 2.35 7x −

13. 244(0.35) 100x 14. 25(0.4) 5x−

15. 5 1 78 2x x− +

Solving LOG INEQUALITIES: Show number line and write answers in INTERVAL NOTATION.

16. 𝑙𝑜𝑔2𝑥 < 3.5 17. 𝑙𝑜𝑔34𝑥 + 7 ≤ 12

18. 𝑙𝑜𝑔9(𝑥 − 1) ≥ 1.5 19. 4𝑙𝑜𝑔33𝑥 − 4 ≤ 7

20. ln 𝑥 + 1 ≥ 2 21. 𝑙𝑜𝑔5(𝑥 − 4) + 6 ≤ 8

22. ln 3𝑥 + 3 < 8 23. −4𝑙𝑜𝑔2𝑥 > 2𝑥 − 7