Question

# 2. The growth of cable television between 1978 and 1994 can be modeled by the following...

2. The growth of cable television between 1978 and 1994 can be modeled by the following logistic function: S(t) = 65/ 1+23e^(-0.214t) where S(t) is the number of cable TV subscribers (in millions) t years after 1970. a. Determine the number of cable TV subscribers in 1984 according to this model. b. Determine S′(t) using the function above and the derivative rules you know.

c. Use this function to determine the rate at which the number of cable TV subscribers was changing in the year 1984.

d. Now write S′(t) by using the logistic differential equation. e. Show that this equation gives you the same result as you got in part c (Use all decimal places of accuracy you can for the number of subscribers in 1984).

f. Determine to the nearest month when the number of cable TV subscribers was increasing most rapidly. Show all work.

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