How do you find a natural growth function? Ex. E(t)?

Answer 1

By solving the differential equation dE/dt = rE
Where r is the rate of growth.

dE/E = r dt
integrate both sides.
ln|E| = rt + d (d is a contant)
exponentiate
|E| = e^(rt+d) = e^d * e^(rt)
E = ± e^d * e^(rt)
We can choose a new constant c equal to ±e^d
E(t) = c * e^(rt)
The constant c will depend on your intial value of E