The total number of people infected with a virus often grows like a logistic curve. Suppose that 25 people originally have the virus, and that in the early stages of the virus (with time, \(t\text{,}\) measured in weeks), the number of people infected is increasing exponentially with \(k=1.8\text{.}\) It is estimated that, in the long run, approximately 7250 people become infected.

*(a)* Use this information to find a logistic function to model this situation.

\(P =\)

*(b)* Sketch a graph of your answer to part (a). Use your graph to estimate the length of time until the rate at which people are becoming infected starts to decrease. What is the vertical coordinate at this point?

vertical coordinate =