Suppose $\backslash$$$15,000$ is invested in an account that earns $4\mathrm{.}6\backslash \%$ interest.

$($a$)$ Write an equation for a function $\backslash ($ V $\backslash )$ that gives the value of the account after $\backslash ($ t $\backslash )$ years if interest is compounded monthly.

$\backslash [$

V$($t$)=$

$\backslash ]$

Your answer cannot be understood or graded. More Information

$($b$)$ Compute $\backslash ($ V$^\{\backslash$prime$\}(2\mathrm{.}5)\backslash ).($Round your answer to two decimal places.$)$

$\backslash$$per year

Interpret your answer.

After $2\mathrm{.}5$ years, the value of the account is increasing at a rate of $\backslash$$

$*$ per year.

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