Between $2006$ and $2016,$ the number of applications for patents, N$,$ grew by about $4\mathrm{.}3\%$ per year. That is$,N(1)=0\mathrm{.}043N(1)$

a$)$ Find the function that satisfles this equation. Assume that $t=0$ corresponds to $2006,$ when approximately $445,000$ p$.$

b$)$ Estimate the number of patert applications in $2020.$

c$)$ Estimate the rate of change in the number of patert apclications in $2020.$

a$)N(T)=$