Another calc question?

Question

A flu epidemic breaks out in Preston. Ayman notes the fraction of the population that is infected at time t (in weeks) is given by f(t) = 64t / (8 + t)^2. What is the largest fraction of the population that is infected during the first 10 weeks? Assume that t = o when the epidemic starts.

Answer 1

f(t) = 64t / (8 + t)^2
f'(t) = -2*64t(8 + t)^-3 + 64(8 + t)^-2 = 0
2t(8 + t)^-3 = (8 + t)^-2
2t = 8 + t
t = 8

f(8) = 64*8 / 16^2 = 2

The function is bogus. It needs a scaling factor ≤ 1/2 to keep it from rising above 100% If it were 32t / (8 + t)^2, then on day 8 the infection fraction is 100%.