The formula for exponential growth is V = S x (1+R) T, where S is the starting value, R is the interest rate, T is the number of periods that have elapsed, and V is the current value.

A variable undergoing logistic growth initially grows exponentially. After some time, the rate of growth decreases and the function levels off, forming a sigmoid, or s-shaped curve. For example ...

For example, in the right hand graph of Figure 2 is a population of Paramecium growing in a laboratory culture. The pattern of growth is very close to the pattern of the exponential equation.

From the graph, we can also see that the y-intercept is 6, therefore we can say that the equation of the straight line is \ (y = mx + 6\). Now we need to find the gradient.