51. Population Growth Beginning in the next section we will see that differential equations can be used to describe or model many different physical systems. In this problem, suppose that a model of the growing population of a small community is given by the initial-value problem dP dt =0.15P(t)20, P(0)=100, where P is the number of individuals in the community and time t is measured in years. How fast, that is, at what rate, is the population increasing at t =0? How fast is the population increasing when the population is 500?