Does the Data Set Represent Logistic Growth?
Logistic Growth A pond has duckweed growing on its surface. As the duckweed continues to grow, resources become limited. The limitations cause the growth rate to change. What we see is constrained or logistic growth. The differential equation to describe constrained or logistic growth is: where P represents the population, t represents time, k is a constant related to the rate of growth, and M is a constant that represents the maximum sustainable population. In this differential equation as the value of P is near zero and the value of M-P is near M, the rate of change is similar to normal exponential growth. As the value of P nears M, the rate of change nears zero. This behavior creates a curve with the familiar “S” shape that describes logistic growth. The solution to this differential equation is where P0 is the constant of integration. Looking at this equation does not provide the same intuition about the kind of growth of the population as is given in the differential equation. Dat
