Answer:
t = 13 days
p(13) = 33.47%
Step-by-step explanation:
p(t) is the percentage of the population infected:
p(t) = 7*t*e∧(-t / 13)
where 0 ≤ t ≤ 39 days
we can apply p'(t) = 0 to get number of days where the percentage of infected people is maximum:
p'(t) = (7*t*e∧(-t / 13))' = 7*(t*e∧(-t / 13))' = 7*((t)'*e∧(-t / 13)+t*(e∧(-t / 13)') = 0
⇒ 7*(1*e∧(-t / 13)+t*e∧(-t / 13)*(-1 / 13)) = 7*e∧(-t / 13)*(1 - (t / 13)) = 0
∴ 1 - (t / 13) = 0 ⇒ t = 13 days
then we get the maximum percent of the population infected as follows
p(13) = 7*13*e∧(-13 / 13)
⇒ p(13) = 33.47%
