In $2012,$ the population of a city was $5\mathrm{.}66$ million. The exponential growth rate was $1\mathrm{.}94\%$ per year.

a$)$ Find the exponential growth function.

b$)$ Estimate the population of the city in $2018.$

c$)$ When will the population of the city be $9$ million?

d$)$ Find the doubling time.