The body metabolizes an antibiotic over time (this is why we take it for several days at specified time intervals). Let C'(t) represent the concentration of the antibiotic that remains in the body at time t, where t is measured in hours after the dose has been taken. Assume the rate of change of the concentration is proportional to the concentration left in the body. dC (a) Write a differential equation for Use k as your constant of proportionality. dt dC dt (b) Solve the differential equation given that originally there were approximately 2290 milligrams of the antibiotic in the body, but 3 hours later, the concentration was approximately 1870 mg. C(t) = (c) What is the concentration after 5.5 hours? Round to the nearest whole number. mg (d) When the concentration of antibiotic falls below 1634 mg, the patient will need to take another dose to replenish the amount in the body until the infection is cured. At what time does this occur? Round to two decimal places. hours
The body metabolizes an antibiotic over time (this is why we take it for several days at specified time intervals). Let C'(t) represent the concentration of the antibiotic that remains in the body at time t, where t is measured in hours after the dose has been taken. Assume the rate of change of the concentration is proportional to the concentration left in the body. dC (a) Write a differential equation for Use k as your constant of proportionality. dt dC dt (b) Solve the differential equation given that originally there were approximately 2290 milligrams of the antibiotic in the body, but 3 hours later, the concentration was approximately 1870 mg. C(t) = (c) What is the concentration after 5.5 hours? Round to the nearest whole number. mg (d) When the concentration of antibiotic falls below 1634 mg, the patient will need to take another dose to replenish the amount in the body until the infection is cured. At what time does this occur? Round to two decimal places. hours
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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Transcribed Image Text:The body metabolizes an antibiotic over time (this is why we take it for several days at
specified time intervals). Let C'(t) represent the concentration of the antibiotic that
remains in the body at time t, where t is measured in hours after the dose has been
taken. Assume the rate of change of the concentration is proportional to the
concentration left in the body.
(a) Write a differential equation for
dC
dt
=
C(t)
(b) Solve the differential equation given that originally there were approximately 2290
milligrams of the antibiotic in the body, but 3 hours later, the concentration was
approximately 1870 mg.
=
dC
dt
mg
Use k as your constant of proportionality.
(c) What is the concentration after 5.5 hours? Round to the nearest whole number.
hours
(d) When the concentration of antibiotic falls below 1634 mg, the patient will need to
take another dose to replenish the amount in the body until the infection is cured. At
what time does this occur? Round to two decimal places.
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