Exam 3: Exponential, Logistic, and Logarithmic Functions

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

A single-cell amoeba doubles every 4 days. How long would it take one amoeba to produce a population of about 10,000 amoebae?

What is the natural logarithmic regression equation for the following data? Estimate the y -value for x=15 . Express answers to the nearest hundredth. x 2 4 7 10 y 3 8 11 12

A single-cell amoeba doubles every 3 days. How long would it take one amoeba to produce a population of about 10,000 amoebae?

Show that $f(x)=\frac{1}{5} \ln x \text { and } g(x)=e^{5 x}$ are inverse functions.

Solve for $x: 3^{2 x-1}=27$

Rosita deposits $\$ 250$ each month into a retirement account that pays $6.00 \%$ APR $(0.50 \%$ per month). What is the value of this annuity after 20 years?

Solve the equation 7-4 log x=10 . Give an exact answer as well as its decimal approximation (to the nearest hundredth).

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

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

Let $S=a(1.08)^{t}$ Solve for t .

Describe the transformations that an be used to transform the graph of $y=\log _{2} x$ to $y=-\log _{2}(x+4)$ . Plot the graph of $y=\log _{2}(x+4)$ .