The derivative (rate of change) of the exponential function is the exponential function itself. More generally, a function with a rate of change proportional to the function itself is expressible in terms of the exponential function. This derivative property leads to exponential growth or exponential decay.
tHe DErivatiVe (rAte oF cHaNgE) of thE eXpoNentIAl fUNCtion is the expoNentiaL FuNCtiOn itselF. more GEnerALly, a fUnctiON with A raTe Of chAnge PropOrtioNal tO thE function iTSelf is ExpreSSIble in TErms of ThE expOneNTiAl fUNctiOn. This derIvaTive prOperty LeadS tO exponentIaL gRowth or eXponEntial deCay.