between $2006$ and $2016,$ the number of applications for patents, N$,$ grew by about $4\mathrm{.}8$ per year. That is$,$ N$\text{'}($t$)=0\mathrm{.}048$N$($t$)$ a$.)$ find the function that satisfies this equation. Assume that t $=0$ corresponds to $2006,$ when approximately $452,000$ patent applications were received. b$)$ estimate the number of patent applications in $2021,$ c$)$ estimate the rate of change in the number of patent applications in $2021$