Let g$($t$)$ be the population $($in thousands of people$)$ of Calculus City, as a function the time t $($in

years$),$ where t $=0$ corresponds to the year $2020.$ In $2020,$ the population was $10000,$ and each year

the population increases by $30\%.$

$($a$)$ Model the population by finding a formula for g$($t$),$ using the appropriate choice of a linear,

polynomial, power, trigonometric, or exponential function, or a piecewise combination thereof.

$($b$)$ Evaluate the expression g$(6),$ and write a sentence explaining what this means.

$($c$)$ Solve the equation g$($t$)=16\mathrm{.}9,$ and write a sentence explaining what this means