A cup of coffee contains about 100 mg of caffeine. Caffeine
is metabolized and leaves the body at a continuous rate of about 17% every hour.

(a) Write a differential equation for the amount, A, of caffeine in the body as a function of the number of hours, t, since the coffee was consumed.
(b) Use the differential equation to find dA∕dt at the start of the first hour (right after the coffee is consumed). Use your answer to estimate the change in the amount of caffeine during the first hour.