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. Write a differential equation for the amount, C, of caffeine in the body at time t hours after drinking the green tea. dc = 32 -0.170 O at dc = 12 -0.170 O dt dc = -0.170 dt dc Odt = 0.17C-32 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. O-31.32 mg/hr 0-11.32 mg/hr 0 -3.32 mg/hr -0.68 mg/hr 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. Does the initial amount of caffeine in the body (whether from the first, second or third brew) change the differential equation?

Answer 1

0 Solutions Given that G(E)=32 (0)2t → Foo the groot brew C1E) - 120 .-00172 → Foo the second boei CLE) - uc -0.17€ → Foo the thiod bocw Given that 17% decays in hout dalt) dt -0017* CIZ). S acct) dt 5-0-178€ In ICLE)) = -0.172 +6 C(E)= ke 0172 Clo): K:32 option Ċ ig corect Answeo. : -017667) dalt dt god bocw C c=ung leave at a sale --(6 * 100 mg per ho [:-0.176({}] :-(4*0.17) * -0.68 mg pet no option 0 55 ccobert Anadoo. -0.68 milho As we have taken snitial amount of coeffcice ag a constante which can be different foo the three, boccao hence. The diffcoential Equation is not affected by the sostial value of Co-Cfficient, vo, The Britab valuc makes no change in the differential og?

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