The total number of students P(t) who have been infected with a virus often grows like a logistic curve. Suppose that 20 students originally have the virus, and that in the early stages of the outbreak (with time, t, measured in weeks), the number of students infected is increasing exponentially with $k = 1.7$. It is estimated that, in the long run, approximately 3750 students will have been infected at some point; this is the carrying capacity.
(a) Use this information to find a logistic function to model this situation. See Formula 7 on p. 673.
P(t) =
(b) Sketch a graph of your answer to part (a). Use your graph to estimate the length of time from the start of the outbreak until the infection rate starts to decrease. What is the population at this inflection point?
Population at inflection point =
