The given function below is approximating the percentage of population infected by a
disease 𝑛 days after it starts spreading in the country.
1/10 𝑝(𝑛) = 𝑛𝑒^(−𝑛/8) for 0 ≤ 𝑛 ≤ 40.
When does the percent of the population infected reach the maximum? What is the
maximum percent (in one decimal place) of the population infected?
p(n) = 10ne^(-n/8)
dp/dn = -5/4 (n-8) e^(-n/8)
dp/dn=0 when n=8, so p(8) = 80/e