Many environmental and biological processes follow first-order kinetics, where the rate of change is proportional to its current state. This is often the case whether it is the change in a concentration of a chemical or the growth or decline of a biological population. The rate of change may be affected by a variety of factors, such as temperature, light intensity or abundance of food, that follow a probability distribution. The moment generating function provides a quick method to estimate the mean and variance of the process through time. This allows valuable insights for environmental risk assessment or population forecasting.