Exponential, Inverse, & Logarithmic Functions

Name______Date______Class______Unit 4 Review Exponential, Inverse, & Logarithmic Functions Tell whether the function shows growth or decay. 1a. j(x)  3(0.04)x 1b. k(x)  5(1.4)x 1c. p(x)  0.25(6)x ______

Tell whether the function is an exponential function. Write yes or no. 5 x x 2a. f (x)  2x  9 2b. g(x)  0.2(5) 2c. h(x)  10(2.2)

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Solve.

3. Colleen’s station wagon is depreciating at a rate of 9% per year. She paid $24,500 for it in 2002. What will the car be worth in 2008 to the nearest hundred dollars?

4. A parcel of land Jason bought in 2000 for $100,000 is appreciating in value at a rate of about 4% each year. In what year will the land double its value?

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Use inverse operations to write the inverse of each function.

x 3x  1 5. f (x)  12  9x 6. f( x )   7. f( x )  12 6

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8. Graph the function. Then write and graph its inverse. Label three points on each graph.

5 f( x ) x  2 2

Write each exponential equation in logarithmic form. Write each logarithmic equation in exponential form.

7 9a. 3  2187 9b. log4 1024  5 9c. log9 729  3

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10. Evaluate. log5 625 11. log8 1 ______

12. Use the given x-values to graph each function. Then graph its inverse. Describe the domain and range of the inverse function. x 1  f( x )    ; x  3, 2, 1, 0, 1, 2, 3 2 

Domain: ______

Range: ______

Condense. Simplify, if possible.

13. log6 8  log6 27 14. log3 6  log3 13.5 15. log4 32  log4 128 ______

16. log2 1920  log2 30 17. log3 486  log3 2 18. log6 180  log6 5 ______

Simplify, if possible. 6 x - 5 log 30 19. log4 4 20. log5 5 21. 7 7 ______

Evaluate. Round to the nearest hundredth.

22. log12 1 23. log3 30 24. log5 10 ______

Solve and check.

25. 122x - 8  15 26. log x  log 10  14 27. 165x  64x + 7

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28. Use a table and graph to solve.

2 x - 5  64 ______

29. Simplify. a. ln ex + 2 b. eln 2x c. e7 ln x ______

Solve. 30. Use the formula A  P ert to compute the total amount for an investment of $4500 at 5% interest compounded continuously for 6 years. ______