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.

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

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?

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, $\left.T(t)=T_{m}+\left(T_{0}-T_{m}\right) e^{-k t} .\right)$

Solve the logarithmic equation log (x+2)+log x=3 log 2 algebraically. Identify any extraneous solutions.

What is the value of $\log _{5} 14$ , accurate to two decimal places?

Graph the logistic function $f(x)=\frac{15}{1+e^{-2 x}}$ Show the viewing window dimensions.

Find the interval(s) where the function $f(x)=3^{-x}$ is decreasing.

Find the value of an investment of $\$ 5200$ invested for 5 years, compounded monthly at the rate of $9.5 \%$ APR.

Solve the logarithmic equation $\log _{x} 5=3$ for x . Leave the answer in radical form.

Which equation is equivalent to $y=7 x^{5} ?$

How long will it take an investment of $750 at 8.75% APR compounded quarterly to grow a $1000?

Determine the domain of the function $f(x)=\ln \left(4 x-x^{2}\right)$

A $\$ 125,000$ mortgage requires monthly payments for 30 years at $7.5 \%$ APR. How much is each payment?

$\text { Describe the end behavior of the function }$ $g(x)=\left(\frac{2}{3}\right)^{x}$ g(x) \rightarrow ---------- as x \rightarrow-\infty g(x) \rightarrow ---------- as x \rightarrow\infty

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?

Which expression is equivalent to ln $\sqrt[5]{\frac{x}{10}} ?$

Write the exponential equation $3^{x}=9$ in logarithmic form.

Solve $e^{x^{2}}+5 x-1=0$ graphically.

List the transformations used to obtain the graph of $g(x)=5 \ln (x-1)+3$ from the graph of $f(x)=\ln x$