The body metabolizes an antiobiotic over time (this is why we take it for several days...

 

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The body metabolizes an antiobiotic 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 Use k as your constant of proportionality. dC dt dC dt mg . (b) Solve the differential equation given that originally there were approximately 2480 milligrams of the antibiotic in the body, but 1 hours later, the concentration was approximately 1890 mg. C(t)= (c) What is the concentration after 7 hours? Round to the nearest whole number. (d) When the concentration of antibiotic falls below 837 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? The body metabolizes an antiobiotic 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 Use k as your constant of proportionality. dC dt dC dt mg . (b) Solve the differential equation given that originally there were approximately 2480 milligrams of the antibiotic in the body, but 1 hours later, the concentration was approximately 1890 mg. C(t)= (c) What is the concentration after 7 hours? Round to the nearest whole number. (d) When the concentration of antibiotic falls below 837 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?

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20 to do Fal 19 C Silving to differenhal equation We have Given CCB in eq ... View the full answer