A cup of green tea contains 32 mg of caffeine when you are using the tea leaves for the first time. A cup from the second brew contains 12 mg of caffeine, while a cup from the third brew contains only 4 mg of caffeine. Caffeine leaves the body at a continuous rate of about 17% per hour.
a) Write a differential equation for the amount, C, of caffeine in the body at time t hours after drinking the green tea.
b) Use the differential equation to find at the start of the first hour (right after drinking the tea) for a cup from the first brew, and use your answer to estimate the change in caffeine in the body during the first hour.
c) Does the initial amount of caffeine in the body (whether from the first, second or third brew) change the differential equation?

Question

A cup of green tea contains 32 mg of caffeine when you are using the tea leaves for the first time. A cup from the second brew contains 12 mg of caffeine, while a cup from the third brew contains only 4 mg of caffeine. Caffeine leaves the body at a continuous rate of about 17% per hour.
a) Write a differential equation for the amount, C, of caffeine in the body at time t hours after drinking the green tea.
b) Use the differential equation to find  at the start of the first hour (right after drinking the tea) for a cup from the first brew, and use your answer to estimate the change in caffeine in the body during the first hour.
c) Does the initial amount of caffeine in the body (whether from the first, second or third brew) change the differential equation?

Quizplus · Accepted Answer

The Answer of A cup of green tea contains 32 mg of caffeine when you are using the tea leaves for the first time. A cup from the second brew contains 12 mg of caffeine, while a cup from the third brew contains only 4 mg of caffeine. Caffeine leaves the body at a continuous rate of about 17% per hour.
a) Write a differential equation for the amount, C, of caffeine in the body at time t hours after drinking the green tea.
b) Use the differential equation to find  at the start of the first hour (right after drinking the tea) for a cup from the first brew, and use your answer to estimate the change in caffeine in the body during the first hour.
c) Does the initial amount of caffeine in the body (whether from the first, second or third brew) change the differential equation?

A Cup of Green Tea Contains 32 Mg of Caffeine