The formula A = 5e^-0.88t can be used to determine the number of milligrams A, o

Question

The formula A = 5e^-0.88t can be used to determine the number of milligrams A, of a certain drug in a patient's bloodstream t hours after the drug has been administered. a. How many milligrams of the drug were initially given to the patient? milligrams b. When the number of milligrams of the drug reaches 3.6, the drug is to be administered again. How many hours will elapse between injections? hours c. Does the number of hours between injections depend on the initial amount of the drug given to the patient?

Explanation / Answer

Solution:

(a)

A= 5e-0.88t

for initial condition we must plug time t =0

therefore

A = 5 e0

A= 5 miligrams

5 miligrams of the drug were initially given to the paitent

Answer: 5

(B)

time when A = 3.6 miligrams

Plug A = 3.6 and calculate the hours elapse between injection

3.6 = 5 e-0.88t

e-0.88t = 3.6/5 =.72

taking log on both side

ln e-0.88t = ln(0.72)

-0.88t = -0.3285

t = 0.373 hours

answer

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