Exam 3: Exponential, Logistic, and Logarithmic Functions

A pie is removed from a $375^{\circ} \mathrm{C}$ oven and cools to $215^{\circ} \mathrm{F}$ after 15 minutes in a room at $72^{\circ} \mathrm{F}$ How long (from the time it is removed from the oven) will it take the pie to cool to $120^{\circ} \mathrm{F} \text { ? }$

Solve for $x: 2^{3 x-1}=16$

A certain company estimates that the computer they plan to buy in 18 months will cost $\$ 4,200$ . How much money should be deposited now into an account paying $5.75 \%$ interest, compounded monthly so there will be enough money to pay cash for the computer in 18 months?

Describe the transformations that can be used to transform the graph of $y=\log _{3} x$ to $y=\log _{3}(x+2)+1$ . Plot the graph of $y=\log _{3}(x+2)+1$

Solve the equation 8 - 3 ln x = 12. Give an exact answer as well as its decimal approximation (to the nearest hundredth).

Graph the function $y=0.25^{x}$

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?

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

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

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

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

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?

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

For the function $f(x)=\frac{6}{1+2 e^{-3 x}}$ (a) Find the horizontal asymptotes. (b) Find the domain and range (c) Describe the end behavior.

A certain company estimates that the computer they plan to buy in 30 months will cost $5,250. How much money should be deposited now into an account paying 6.25% interest, compounded monthly so there will be enough money to pay cash for the computer in 30 months?

For the function $f(x)=\frac{5}{1+4 e^{-2 x}}$ : (a) Find the horizontal asymptotes. (b) Find the domain and range. (c) Describe the end behavior.

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

(a) Solve for $x: \log _{3} 81=x$ (b) Solve for $x: \log _{x} 8=\frac{3}{2}$

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

When Jose was born, his grandmother deposited $8,000 into an account paying 6% interest, compounded quarterly. How much money will be available to use for college tuition 18 years later?