Hi!

Suppose that a population insects doubles every 5 hours. If you start with 6000 insects:

Find an expression for the number of insects present in $\displaystyle h$ hours.

$\displaystyle n(h) = n_0 e^\text{rh}$

$\displaystyle n(h) = 6000e^{5\text{h}}$

$\displaystyle \frac{n(h)}{6000} = e^{5\text{h}}$

$\displaystyle \ln\left(\frac{n(h)}{6000}\right) = 5\text{h}$

$\displaystyle \frac15\ln\left(\frac{n(h)}{6000}\right) = h$