Properties of Integrating Exponential Functions

I. For an exponential growth function given by $P(t)=P_0e^{kt}$ (with $k>0$), the integral over a time interval represents the accumulated total value of $P(t)$ over that period, not merely its final value.

II. Regardless of whether the exponent is positive or negative, the average value of an exponential function over a long interval always tends to infinity.

III. When integrating an exponential function with a coefficient in the exponent other than 1, the antiderivative must include division by that coefficient (due to the chain rule).

Which of the above statements regarding exponential functions and integration is/are true?