How do you determine the multiplier for exponential growth and decay?

1 Answer
Apr 23, 2015

For an exponential model P=f(t)=P0ekt, where P0 is the initial value (at time t=0). You can find the value of k if you know another data point by using logarithms.

For example, if P=f(t)=100ekt and you know f(3)=200, then 200=100e3k so that e3k=2, 3k=ln(2), and k=13ln(2)0.231=23.1%. This represents an "instantaneous relative rate of change".

In general, if you are given the data point (t1,P1), where t1 is not zero (in addition to the data point (0,P0)), then P1=P0ekt1 so that k=1t1ln(P1P0).