A flu epidemic breaks out in a city. The fraction of the population that is infected at time t, in weeks, is given by the function f(t)=64t/(8+t)^3. What is the largest fraction of the population that is infected during the first 10 weeks? Assume that t=0 when the epidemic starts.
Ok.. I think I have my method correct for this, but I am not exactly sure, so can someone verify my method and calculations to see if I have the correct answer? Thank you very much in advance
f'(t)=0 when t = -5 or t = -8
f'(t)=undefined when t = -8
Reject answers above because all negative.. time cannot be negative
In this case, domain is 0<=t<=10.. therefore
Test end points
Therefore the largest fraction of the population that is infected during the first ten weeks is 0.1097 when it is the tenth week.