A curve representing the total number of people, P, infected with a virus often has the shape of a logistic curve of the form P= 1+C with time t in wecks. Suppose that 12 people originally have the virus and that in the carly stages the number of people infected is increasing approximately cxponentially, with a continuous growth rate of 1.78. It is estimated that, in the long-run, approximately 6000 people will become infected. (a) What should we use for the parameters k and L? Enter the exact answers k = Number L = Number (b) Use the fact that when = 0, we have P = 12. lo find C. Enter the exact answer. C = Number (e) Now that you have estimated L, k, and C, what is the logistic function you are using to model the data? Enclosc arguments of functions, numcrators, and denominators in parentheses. For example, sin (2x) or (a - b)/(1+n). P(t) = Q (d) Estimate the length of time until the rate at which people are becoming infected starts to decrease. What is the value of Pat this point? Round your answer fort to onc decimal place and your answer for P to the nearest hundred people. t Number P Number
