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}}).
