7 Mid-Chapter Quiz

Do you know HOW?

Determine whether each function is an example of exponential growth or decay. Then find the y-intercept.

1. y = 100 ( 0.25 ) x y equals 100 . open , 0.25 , close to the x
2. y = 0.6 ( 1 10 ) x y equals 0.6 . open , 1 tenth , close to the x
3. y = 7 8 ( 18 ) x y equals , 7 eighths . open 18 close to the x

Graph each function. Then find the domain, range, and y-intercept.

4. y = − 4 ( 2 ) x y equals negative 4 . open 2 close to the x
5. y = 1 4 ( 10 ) x y equals , 1 fourth . open 10 close to the x
6. y = 8 ( 0.25 ) 25 y equals 8 . open , 0.25 , close to the twenty fifth
7. Investment Suppose you deposit $600 into a savings account that pays 3.9% annual interest. How much will you have in the account after 3 years if no money is added or withdrawn?
8. Depreciation The initial value of a car is $25,000. After one year, the value of the car is $21,250. Write an exponential function to model the expected value of the car. Estimate the value of the car after 5 years.

Graph each function as a transformation of its parent function. Write the parent function.

9. y = 3 x − 2 y equals , 3 to the x , minus 2
10. y = 1 4 ( 5 ) x − 1 + 4 y equals , 1 fourth . open 5 close super x minus 1 end super . plus 4
11. y = − ( 0.5 ) x + 3 y equals negative . open 0.5 close super x plus 3 end super
12. y = − 6 ( 3 4 ) x − 10 y equals negative 6 . open , 3 fourths , close to the x . minus 10

Evaluate each expression to four decimal places.

13. e 5 e to the fifth
14. e 3 2 e super 3 halves end super
15. e − 4 e super negative 4 end super

Find the amount in a continuously compounded account for the given conditions.

16. principal: $500; annual interest rate: 4.9%; time: 2.5 years
17. principal: $6000; annual interest rate: 6.8%; time: 10 years

Write each equation in logarithmic form.

18. 10 4 = 10 , 10 to the fourth , equals 10 comma 000
19. 1 4 = 4 − 1 1 fourth , equals , 4 super negative 1 end super
20. 8 = ( 1 2 ) − 3 8 equals . open , 1 half , close super negative 3 end super

Evaluate each logarithm.

21. log 8 64 log base 8 , 64
22. log 4 ( 256 ) log base 4 , open 256 close
23. log 1 5 625 log base 1 fifth . 625

Graph each logarithmic function. Find the domain and range.

24. y = log 5 ( x − 1 ) y equals , log base 5 , open x minus 1 close
25. y = 4 log x + 5 y equals 4 log x plus 5
26. Crafts For glass to be shaped, its temperature must stay above 1200°F. The temperature of a piece of glass is 2200°F when it comes out of the furnace. The table shows temperature readings for the glass. Write an exponential model for this data set and then find how long it takes for the piece of glass to cool to 1200°F.

Do you UNDERSTAND?

27. Error Analysis A student claims the y-intercept of the graph of the function y = a b x y equals , eh b to the x  is the point (0, b). What is the student's mistake? What is the actual y-intercept?
28. Writing Without graphing, how can you tell whether an exponential function represents exponential growth or exponential decay?
29. Compare and Contrast Compare the graph of y = log 3 ( x + 1 ) y equals , log base 3 , open x plus 1 close  to the graph of its inverse y = 3 x − 1 . y equals , 3 to the x , minus 1 .  How are the graphs alike? How are they different?
30. Vocabulary Explain how the continuously compounded interest formula differs from the annually compounded interest formula.

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