• A bank features a savings account that compounds interest semi-annually.
The account balance can be modeled by the exponential formula $S(t) = P(1 + \frac{r}{n})^{nt}$, where $S$ is the
future value, $P$ is the present value, $r$ is the annual percentage rate written as a decimal, $n$ is the
number of times each year that the interest is compounded, and $t$ is the time in years.
If an initial blance of $5,200 is deposited, then what is the rate if the account has a
balance of $12,000 after 8 years?
• A population of bacteria is growing according to the $P(t) = 32e^{0.254t}$. Determine how many
years it will take for the population to exceed 3500.
