# An initial population of 175 quail increases at an annual rate of 22%. Write an exponential function to model the quail population. What will the approximate population be after 5 years?

Aug 8, 2016

472

#### Explanation:

$N = {N}_{0} {e}^{k t}$

Take $t$ in years, then at $t = 1$, $N = 1.22 {N}_{0}$

$1.22 = {e}^{k}$

$\ln \left(1.22\right) = k$

$N \left(t\right) = {N}_{0} {e}^{\ln \left(1.22\right) t}$

$N \left(5\right) = 175 \cdot {e}^{\ln \left(1.22\right) \cdot 5} = 472.97$

$\implies 472$ quail