Chapter 7 Review Part I
Determine whether the function represents exponential growth or exponential decay. Graph the function.
Determine the domain and range.
x
1. y = 5
2
2. y  3    2
3
x
3
5. y  2  
4
x
7
6. y   
2
1
3. y   
5
x
1
4. y    3x  2
3
x
7. y  2 4
x2
1
1
8. y  2  
3
x2
1
9. A new laptop computer costs $1500. The value of the computer decreases by 22% each year. Write a model
giving the computer’s value v after t years. Estimate the value of the computer after 2 years.
10. You deposit $2000 into an account that pays 4% interest annually. Write a model showing the amount of
money in the account A after t years. Estimate how much money will be in the account after 8 years.
11. The area of a wound decreases exponentially with time. The area A of the wound after t days can be
modeled by A = a•e -0.05t, where a is the initial wound area. If the initial wound area is 4 square centimeters,
what is the area after 14 days?
Rewrite into exponential form. Then find the value of the variable.
12. log 3 81 = x
13. log 7 7 = y
14. log 14 x = 0
15. log 1/2 32 = y
16. log 16 2 = x
17. log X 32 = 5
18. log 64 8 = x
Chapter 7 Review Part II
Rewrite the equation in exponential form.
1. log 7 49 = 2
2. log 2 16 = 4
3. log 16 4 = 1/2
Evaluate the logarithm without using a calculator.
1
5. log 9 81
6. log 3
7. log 2 4
3
Find the inverse of the function.
9. y = log 3 x
10. y = ln x
11. y = 4x – 5
Expand.
13. log 2 (8x)
14. ln 3xy2
Condense.
17. log 3 – log 5x
18. 3log 2 5 + log 2 x + 2log 2 y
15. log 4 4yz3
Rewrite AND evaluate (to three decimal places).
20. log 3 30
21. log 5 10
22. log 3 0.7
4. log 5 125 = 3
8. log 5 1
12. y = 2x + 6
16. log 6 x2y3
19. ln x – 2 ln y + ln 4
23. log 1.23 5.38
Solve the exponential or logarithmic equation. Check for extraneous solutions. Round the result to three
decimal places if necessary.
23. log 3 (x + 10) = log 3 (2 - 3x)
24. 4x = 16 (x – 1)
25. 10x – 1 - 12 = 22 26. log x + log (x + 3) = 1