Calculus~ logistic growth!!!?

Question

1. What is a logistic growth?

2. Give real life applications of Logistic Growth, (We sometimes call Logistic Growth the curve of Learning).

3. Plot the graph of its general equation y = a/(1+b·e^-kx) and

o What is the y intercept ? Any x intercepts?

o Any Horizontal asymptotes?

o Note (for any logistic applications the domain is x > or = 0).

Answer 1

1. Growth where the rate of growth is proportional to the product of the existing population and the available resources. Usually resouces are expressed in terms of the "carrying capacity" C, which is the maximum population sustainable. The equation then has form dy/dx = ky(C-y).

2. Population growth in a fixed area is the classic example, but applies to many situations where there is a fixed maximum.

3. I won't try to draw the graph, but it has an 'S' type of shape; it starts off looking like exponential growth, but then slows down and approaches a ceiling. From the equation you can see that the y intercept is a/(1+b) and there is no x intercept, and the horizontal asymptote as x->∞ is y = a.

Answer 2

I have included a reference.