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# Quiz 3: Exponential, Logistic, and Logarithmic Functions

The population of Powerville is 425,000 , and it is increasing at a rate of 4.2% each year. Predict the number of years until the population will be 750,000 . Round to two decimal places.
(Short Answer)

Answer:

13.81 years

$\text { Write the inverse of the function } f(x)=e^{x+2} \text {. }$
(Short Answer)

Answer:

$f^{-1}(x)=\ln x-2$

Juan contributes $\ 65$ monthly into an IRA annuity for 20 years. If the account earns 5.6\% annual interest compounded monthly, what is the value of Juan's account after 20 years?
(Short Answer)

Answer:

$\ 28,649.40$

A casserole is removed from a $375^{\circ} \mathrm{F}$ oven, and it cools to $200^{\circ} \mathrm{F}$ after 15 minutes in a $75^{\circ} \mathrm{F}$ room. How long (from the time it is taken out of the oven) does it take to cool to $100^{\circ} \mathrm{F} ?$ (Hint: Use Newton's Law of Cooling, $\left.T(t)=T_{m}+\left(T_{0}-T_{m}\right) e^{-k t} .\right)$
(Short Answer)
Solve the logarithmic equation log (x+2)+log x=3 log 2 algebraically. Identify any extraneous solutions.
(Short Answer)
Correct Answer:

x=2 ; Ex...

What is the value of $\log _{5} 14$ , accurate to two decimal places?
(Short Answer)
Graph the logistic function $f(x)=\frac{15}{1+e^{-2 x}}$ Show the viewing window dimensions.
(Essay)
Find the interval(s) where the function $f(x)=3^{-x}$ is decreasing.
(Multiple Choice)
Find the value of an investment of $\ 5200$ invested for 5 years, compounded monthly at the rate of $9.5 \%$ APR.
(Short Answer)
Solve the logarithmic equation $\log _{x} 5=3$ for x . Leave the answer in radical form.
(Short Answer)
Which equation is equivalent to $y=7 x^{5} ?$
(Multiple Choice)
How long will it take an investment of $750 at 8.75% APR compounded quarterly to grow a$1000?
(Short Answer)
Determine the domain of the function $f(x)=\ln \left(4 x-x^{2}\right)$
(Multiple Choice)
A $\ 125,000$ mortgage requires monthly payments for 30 years at $7.5 \%$ APR. How much is each payment?
(Short Answer)
$\text { Describe the end behavior of the function }$ $g(x)=\left(\frac{2}{3}\right)^{x}$ g(x) \rightarrow ---------- as x \rightarrow-\infty g(x) \rightarrow ---------- as x \rightarrow\infty
(Essay)
Correct Answer:

\(\begin{array}{l}
g(x) \rightarrow \und...

A bank advertises that currently a CD pays 6 % APR compounded daily (use 365 days a year). What is the effective yield on this CD, to the nearest hundredth?
(Short Answer)
Which expression is equivalent to ln $\sqrt[5]{\frac{x}{10}} ?$
(Multiple Choice)
Write the exponential equation $3^{x}=9$ in logarithmic form.
(Short Answer)
Solve $e^{x^{2}}+5 x-1=0$ graphically.
(Short Answer)
List the transformations used to obtain the graph of $g(x)=5 \ln (x-1)+3$ from the graph of $f(x)=\ln x$
(Essay)
Correct Answer:

Vertical stretch by a factor o...

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