Help solve for parts A through C.

Between 2006 and 2016, the number of applications for patents, N, grew by about 3.2% per year. That is, N'(t) = 0.032N(t). a) Find the function that satisfies this equation. Assume that t = 0 corresponds to 2006, when approximately 461,000 patent applications were received. b) Estimate the number of patent applications in 2020. c) Estimate the rate of change in the number of patent applications in 2020