Question

Question Completion Status: QUESTION 2 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. Use the differential equation to find dC/dt at the start of the first hour (right after the tea is consumed) for a cup from the third brew, and use your answer to estimate the change in caffeine in the body during the first hour. 0-31.32 mg/hr 0-11.32 mg/hr 0 -3.32 mg/hr -0.68 mg/hr Click Save and Submit to save and submit. Click Save All Answers to save all answers Save All Answers Save and

Answer 1

let the amount of caffeine in the body at time t es c leaves It is given that caffeine the body at a continuous rate of 17). Per hom. In other words. rate of change in. С is. -0.17 C. 1 dc dt = -0.17.C dc = (separating) -0.17dt С on integration s de = - 01 - 0 > luc= -0.17tt en a where ls constant

T en 등 encoln a= -0.17+ -0.174 both side taking exponential - e-0.177 ulo C ae-0.17t Initially at t-O 4 aeo =a a c = 4 e. -0.15 taking derivative of above da -0.17+ (-0.17) 4 (-0.17) 4 eno. -0.68 so, the change in caffeine in the body in first tirst hour n. -0.68 mg Ihr. last option is correct.