Precalculus by Richard Wright

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3-Review

Take this test as you would take a test in class. When you are finished, check your work against the answers. On this assignment round your answers to three decimal places unless otherwise directed.

1. Simplify
2. 4 log₃ 3^2x
3. 4 ⋅ 5^{log₅ 3t}
4. Identify the asymptote, domain, and range. Then graph the function.
5. f(x) = 2 ⋅ 3^{x − 1} − 4
6. g(x) = ½ ln (x + 2) + 1
7. Evaluate
8. log₂ 32
9. log_½ 8
10. 3^⅓
11. Expand ${log}_4\frac{16x^2{y}^3}{x^4{z}^5}$
12. Condense 3 log x − 2 log y + log z
13. Solve
14. 3^x = 81
15. 2^{x + 8} = 16
16. 3 ⋅ 5^x − 2 = 10
17. 4e^{2x − 1} = 16
18. log₅ (x + 1) = 3
19. 2 log (x + 3) + 4 = 15
20. ln (x) + ln (x + 3) = 4
21. An archaeologist finds a mummy whose body contains 68% of the carbon-14 found in living bodies. If the half-life of carbon-14 is 5730 years, how old is the mummy?
22. In electronics, a capacitor can act as a small battery. If a charged capacitor is used to power a circuit, the function V = V₀e^−t/τ models the voltage of the capacitor. V₀ is the initial voltage, τ is the time constant, and t is the time in seconds.
23. If the initial voltage is 12V and the voltage is 4V after 1.5 s, find an equation to model the capacitor.
24. How long for the capacitor to discharge to 2V?
25. What will the voltage be after 1.3 s?

Answers

1. 8x
2. 12t
3. HA: y = −4; Domain: (−∞, ∞); Range: (−4, ∞);

   

4. VA: x = −2; Domain: (−2, ∞); Range: (−∞, ∞);

   

5. 5
6. −3
7. 1.442
8. 2 + 3 log₄ y − 2 log₄ x − 5 log₄ z
9. $log\frac{x^{3}z}{y^2}$
10. 4
11. −4
12. 0.861
13. 1.193
14. 124
15. 316224.766
16. 6.040
17. 3188 years
18. V = 12e^−t/1.37
19. 2.45 s
20. 4.65 V