Answer to Question #319845 in Differential Equations for Almas

Question

Applications of Differential Equation of Population Growth

Answer 1

It is possible to explain the various growth phenomena with mathematical model, some of them are simple and some are complicated. The most famous example is the familiar Malthusian or exponential growth model; in differential equation form it has the equation:

$$\dfrac{dP}{dT}=KP$$

Where, P is the magnitude of growing quantity, T is the time and K is the growth coefficient. The solution to this equation is:

$$P=P_0e^{-at}$$