How do you Find the exponential growth factor?

1 Answer
Sep 27, 2014

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.