An antibiotic is administered intravenously into the bloodstream at a constant rate r. As the drug flows through the patient’s system and acts on the infection that is present, it is removed from the bloodstream at a rate proportional to the amount in the bloodstream at that time. Since the amount of blood in the patient is constant, this means that the concentration y = y(t) of the antibiotic in the bloodstream can be modeled by the differential equation

a. If y(0) = y₀, find the concentration y(t) at any time t. 

b. Assume that y₀y→∞ y(t). Sketch the solution curve for the concentration.

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dy dt =r- - ky, k> 0 and constant.