Chapter 6.9, Problem 76ES

The death rate for victims of a plague during the Bombay epidemic of $1905-1906$ can be modeled by the formula $R\left(t\right)=890{\mathrm{sech}}^2\left(0.2t-3.4\right)$ deaths per week, where $0\le t\le 30$ indicates the number of weeks since the outbreak of the disease. Use this model in each part.

(a) What was the maximum death rate? In what week did it occur?

(b) Estimate the number of deaths that occurred during the $30\text{-week}$ epidemic.