An investor is presented with a choice of two investments: an established clothing store and a new bookstore. Each choice requires the same intial investment and each produces a continuous income stream of $5\%,$ compounded continuously. The rate of flow of income from the clothing store is $f(t)=56897,$ and the rate of flow of income from the bookstore is expected to be $g(t)=48224e^{-0\mathrm{.}03t}.$

A$.$ Find the future value of $f(t)$ after $7$ years and interpret the result. First, write an expression for the definite integral you must evaluate to answer this question.

$dx,$ where $a=$

and $b=$

The future value of the investment after $$ years is $ $$

$($Round your final answer to $4$ significant figures. For example, an answer like $$1,244,252\mathrm{.}02$ would become $$1,244,000\mathrm{.}00.)$

B$.$ Find the future value of $g(t)$ after $7$ years and interpret the result. First, write an expression for the definite integral you must evaluate to answer this question.

${\displaystyle \underset{a}{\overset{b}{}}}dx,$ where $a=$

and $b=$

The future value of the investment after $$ years.$-$is $5($Round your final answer to $4$ significant figures. For example, an answer like $$1,244,252\mathrm{.}02$ would become $$1,244,000\mathrm{.}00.)$