Answer to Question #56240 in Calculus for Olivia

Question

1. Suppose a patient is given a continuous intravenous infusion of glucose at a constant rate of
mg/min. Then, the rate at which the amount of glucose in the bloodstream is changing at
time (in minutes) because of this infusion is given by
A'(t)=re^-at

mg/min, where is a positive constant associated with the rate at which excess glucose is
eliminated from the bloodstream and is dependent on the patient’s metabolism rate.
a) Derive an expression for the amount of glucose in the bloodstream at time t if A(0)=0

b) If and mg/min, find the amount of glucose in the bloodstream 5
minutes after treatment began.