We have been given that function that models the population to be:
p(t)=7te^(-t/12)
we are required to compute for the time taken for the percentage of infected people to be maximum.
from the interval given, the maximum number will be at the point p'(t)
from the function;
p'(t)=-7/12e^(-t/12)(t-12)
equating this to zero and solving for t we get:
-7/12e^(-t/12)(t-12)=0
t=12
hence it will take a maximum of 12 days for infection to reach it's maximum percentage.
