A business is planningto purchase a piece of equipment that will produce a continuous stream of income for $6$ years with rate of flow $f(t)=12348.$ Assume the continuous income stream earns $6\mathrm{.}85\%,$ compounded continuously.

A$.$ Find the future value of $f(t)$ after $6$ years and interpret the result. First, write an expression for the definite integral you must evaluate to answer this question.

$($:${\displaystyle \underset{a}{\overset{\phantom{}}{}}}\}$

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.)$

B$.$ Find the present value of the continuous income stream. That is$,$ what single deposit into an account earning the same interest rate will produce the same future value as the continous income stream?

To answer this question you must solve the equation $($Use $P$ to represent the principal amount invested.$)$

In order to match the $ $$ that will be earned by the continous income stream over

$$ years, you would need a present value $($a single deposit$)$ of $ $$

$($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.)$