Epidemiology—AIDS Cases: One of the primary applications of logistic curves is to model th...

Epidemiology—AIDS Cases: One of the primary applications of logistic curves is to model the spread of disease. During the early 1980s acquired immune deficiency syndrome (AIDS) was introduced to the U.S. population, and the number of cases grew rapidly during that decade. The annual number of new AIDS cases in the United States from 1980 to 1995 can be modeled by

where t represents the number of years since 1980, and f(t) represents the number of new AIDS cases. (Source: Centers for Disease Control and Prevention.)

(a) Use the model to determine the number of new AIDS cases in the United States in 1986.

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(b) Compute the slope of the secant line for x = 6 and Δx = 5 and interpret.

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(c) Determine and interpret.