SOLUTION: Solve for the logistic function with initial condition = 14, limit to growth = 42 and passing through (1, 28) Thank you!

Question 1127178: Solve for the logistic function with initial condition = 14, limit to growth = 42 and passing through (1, 28)
Thank you!
Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

The standard form of a logistic function is

The "ab^x" in the denominator is a decreasing exponential function; as x gets very large that exponential goes to zero, so the denominator goes to 1. That means the numerator c is the limiting value of the function.

So in this example we know the function is of the form

The initial value of the function is when x is 0. When x is 0, the denominator of the function is just 1+a. Use the given initial value to find the value of a.

Now we know the function is of the form

Now, to finish finding the logistic function, find the value of b by using the given data point.

The logistic function for this problem is

A graph, including horizontal lines at the initial, intermediate, and limiting values of 14, 28, and 42:

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