Question

1. Suppose a drug is administered to a patient through an intravenous line at a rate of r mg/hr. The rate at which the drug is metabolized causes the patient to eliminate 5% of the amount of the drug in their system per hour. Let y(t) represent the amount of the drug in the patients system t hours after it began to be administered.  

a) write a first-order differential equation involving the function y that represents the situation along with an appropriate initial condition.

b) solve the differential equation from part (a) using the methods for solving separable differential equations.

c) solve the differential equation from part (a) using the methods for solving linear differential equations.

d) at what rate r should the drug be administered to the patient if the goal is for the quantity of drug in their system to approach 250 mg (assuming the drug continues to be administered indefinitely)?

*Please answer clearly so that I can understand how to do the problem, thank you!

Answer 1