Help! Stuck on a word problem.?

Question

A disease has hit College Station, Texas. The percentage of the population infected t days after the disease arrives is approximated by p(t) = 10t e^-t/8 for 0
a) After how many days is the percentage of infected people a maximum?
b) What is the maximum percent of the population infected?

Any help is appreciated!

Answer 1

Basically, this is a differentiation problem, because you need to take the derivative of p(t) and set it equal to zero in order to find the maximum value of infected people. dp/dt= -10t/8e^(-t/8)+10e^(-t/8)=0 So t=8 (when you solve this).
For b, just calculate p(8)=29.43%.