Precalculus by Richard Wright

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

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 log
_{3}3^{2x} - 4 ⋅ 5
^{log5 3t} - Identify the asymptote, domain, and range. Then graph the function.
*f*(*x*) = 2 ⋅ 3^{x − 1}− 4*g*(*x*) = ½ ln (*x*+ 2) + 1- Evaluate
- log
_{2}32 - log
_{½}8 - 3
^{⅓} - Expand ${log}_{4}\frac{16{x}^{2}{y}^{3}}{{x}^{4}{z}^{5}}$
- Condense 3 log
*x*− 2 log*y*+ log*z* - Solve
- 3
^{x}= 81 - 2
^{x + 8}= 16 - 3 ⋅ 5
^{x}− 2 = 10 - 4
*e*^{2x − 1}= 16 - log
_{5}(*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*=*V*_{0}*e*^{−t/τ}models the voltage of the capacitor.*V*_{0}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?

- 8
*x* - 12
*t* - HA:
*y*= −4; Domain: (−∞, ∞); Range: (−4, ∞); - VA:
*x*= −2; Domain: (−2, ∞); Range: (−∞, ∞); - 5
- −3
- 1.442
- 2 + 3 log
_{4}*y*− 2 log_{4}*x*− 5 log_{4}*z* - $log\frac{{x}^{3}z}{{y}^{2}}$
- 4
- −4
- 0.861
- 1.193
- 124
- 316224.766
- 6.040
- 3188 years
*V*= 12*e*^{−t/1.37}- 2.45 s
- 4.65 V