The reason why exponential functions govern population growth rate is similar to the way spring oscillatorswork. The rate at which a population grows, its rate of change with respect to time, depends on how manyindividuals are in the population to begin with: the more individuals available to procreate the more offspringcan be produced. Therefore, the equation that governs the growth of populations is a function whose rate ofchange (slope) is proportional to itself. This is exactly the definition of an exponential to begin with