person is given an injection of 300 milligrams of penicillin at time t = 0. Let f(t) be the amount (in milligrams) of penicillin present in the person’s bloodstream t hours after the injection. The amount of penicillin decays exponentially with f(t) = 300e −0.6t . (a) Give the differential equation satisfied by f(t) (b) how much penicillin will remain after 5 hours? (c) What is the biological half-life of the penicillin?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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A person is given an injection of 300 milligrams of penicillin at time t = 0. Let f(t) be the
amount (in milligrams) of penicillin present in the person’s bloodstream t hours after the
injection. The amount of penicillin decays exponentially with f(t) = 300e
−0.6t
.
(a) Give the differential equation satisfied by f(t)
(b) how much penicillin will remain after 5 hours?
(c) What is the biological half-life of the penicillin?

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