Daniel Koka, Tutor at Rutgers University, Numerade Educator

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Calculus of a Single Variable

Population Growth When predicting population growth, demographers must consider birth and death rates as well as the net change caused by the difference between the
rates of immigration and emigration. Let $P$ be the population at time $t$ and let $N$ be the net increase per unit time resulting from the difference between immigration and emigration. So, the rate of growth of the population is given by
$$\frac{d P}{d t}=k P+N$$
where $N$ is constant. Solve this differential equation to find $P$ as a function of time, when at time $t=0$ the size of the population is $P_{0} .$

Chapter 6: Differential Equations

Section 4: First-Order Linear Differential Equations