How do you Find the exponential growth factor?

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Answer 1 · 2014-09-27T12:48:28

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.