Between $2006$ and $2016,$ the number of applications for patents, N$,$ grew by about $3\mathrm{.}4\%$ per year. That is$,$ N$\text{'}($t$)=0\mathrm{.}034$N$($t$).$ a$.)$ Find the function that satisifes the equation. Assume that t $=0$ corresponds to $2006,$ when approximately $456,000$ patent applications were received. b$.)$ Esimate the number of patent applicaitons in $2022$ c$.)$ Estimate the rate of change in the number of patent applicaitons in $2022.$