Between

$20062006$

and$2016,$ the number of applications for$$ patents, N$,$ grew by about

$3\mathrm{.}13\mathrm{.}1\%$

per year. That$$ is$,$

Upper N prime left parenthesis t right parenthesisN$($t$)$equals$=0\mathrm{.}0310\mathrm{.}031$Upper N left parenthesis t right parenthesisN$($t$).$

$$a$)$

Find the function that satisfies this equation. Assume that

tequals$=0$

corresponds to

$20062006,$

when approximately

$453,000453,000$

patent applications were received.

$$b$)$

Estimate the number of patent applications in

$20202020.$

$$c$)$

Estimate the rate of change in the number of patent applications in

$20202020.$