Question

How do you Find the exponential growth factor?

Answer 1

I assume that the grwoth factor same as is the growth constant.

Let us look at an example.

`P(t)=P_0e^{kt}`,

where `P_0` is an initial value (`=P(0)`).

To determine `k`, there should be another clue given like its doubling-life. Let us say the doubling-life is 3 years.

`P(3)=P_0e^{k(3)}=2P_0`

by dividing by `P_0`,

`Rightarrow e^{3k}=2`

by taking the natural log,

`Rightarrow ln e^{3k}=ln2`

by simplifying a bit further,

`Rightarrow3k=ln2`

by dividing by 3,

`Rightarrow k={ln2}/3`

I hope that this was helpful.