Continuous growth of a bacterial culture

Statement

A bacterial culture grows as $N(t)=N_0\,e^{0{.}4t}$, with $t$ in hours. If there are $500$ bacteria at the start, how many are there after $6$ hours?

Solution

$N(6)=500\,e^{0{.}4\cdot 6}=500\,e^{2{.}4}=500\cdot 11{.}023176\approx\boxed{5512\ \text{bacteria}}.$