Jesus did many other things as well. If every one of them were written down, I suppose that even the whole world would not have room for the books that would be written. John 21:25 NIV
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.
Simplify
- 4 log3 32x
- 4 ⋅ 5log5 3t
Identify the asymptote, domain, and range. Then graph the function.
- f(x) = 2 ⋅ 3x − 1 − 4
- g(x) = ½ ln (x + 2) + 1
Evaluate
- log2 32
- log½ 8
- 3⅓
- Expand
- Condense 3 log x − 2 log y + log z
Solve
- 3x = 81
- 2x + 8 = 16
- 3 ⋅ 5x − 2 = 10
- 4e2x − 1 = 16
- log5 (x + 1) = 3
- 2 log (x + 3) + 4 = 15
- ln (x) + ln (x + 3) = 4
- 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?
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.
- If the initial voltage is 12V and the voltage is 4V after 1.5 s, find an equation to model the capacitor.
- How long for the capacitor to discharge to 2V?
- What will the voltage be after 1.3 s?
Answers
- 8x
- 12t
- HA: y = −4; Domain: (−∞, ∞); Range: (−4, ∞);
- VA: x = −2; Domain: (−2, ∞); Range: (−∞, ∞);
- 5
- −3
- 1.442
- 2 + 3 log4 y − 2 log4 x − 5 log4 z
- 4
- −4
- 0.861
- 1.193
- 124
- 316224.766
- 6.040
- 3188 years
- V = 12e−t/1.37
- 2.45 s
- 4.65 V