Differential equations.
There are gophers in a very large vacant lot. The original population is 30 Gophers. After 2 months there are 38. When will there be 45 gophers? round answer to nearest tenth of a month
let g(t) = 30e^(kt)
when t=2, g(2) = 38
38 = 30e^2k
1.2666667 = e^2k
2k = ln 1.2666667
k = .11819
so
45 = 30e^.11819t
.11819t = ln(45/30)
t = 3.43 months
or
3.4 months to the nearest tenth