For an exponential model #P=f(t)=P_{0}e^{kt}#, where #P_{0}# 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)=100e^{kt}# and you know #f(3)=200#, then #200=100e^{3k}# so that #e^{3k}=2#, #3k=ln(2)#, and #k=\frac{1}{3}ln(2)\approx 0.231=23.1%#. This represents an "instantaneous relative rate of change".
In general, if you are given the data point #(t_{1},P_{1})#, where #t_{1}# is not zero (in addition to the data point #(0,P_{0})#), then #P_{1}=P_{0}e^{kt_{1}}# so that #k=\frac{1}{t_{1}}ln(\frac{P_{1}}{P_{0}})#.
