Logarithmic Function Problem

The public health service monitors the spread of an epidemic of a particularly long-lasting strain of the flu in a city of 500,000 people using the logistic function. At the begining of the first week (time zero), 200 cases had been reported. During the first week 300 new cases were reported.

a. Determine the logistic function.

b. Estimate the number of individuals infected after 5 weeks.

c. When will the epidemic spread at the greatest rate?

d. At what rate will the epidemic spread when 40% of the population has been infected?

e. Graph the logistic function for the first 20 weeks of the epidemic's spread.