Population Growth Beginning in the next section we will see that differential equati...

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 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?