Between $2006$ and $2016,$ the number of applications for paterits, N$,$ grew by about $4\mathrm{.}3\%$ per year. That is$,N*(4)=0\mathrm{.}043N(4).$

a$)$ Find the function that satisfies this equation. Assume that $t=0$ corresponds to $2006,$ ahen acproximaley $443,000$ patent applications were received.

b$)$ Estimate the number of patent applications in $2021.$

c$)$ Estimale the rate of change in the number of patent applications in $2021.$

a$)N(t)=$

b$)$ The number of patent applications in $2021$ will be $$

$($Round to the nearest whole number as needed.$)$

c$)$ The rate of change in the number of patent applications in $2021$ is about $$

$$

$($Round to the nearest whole number as needed.$)$