When glucose is infused into a person’s bloodstream at a constant rate of c grams per minute, the glucose is converted and removed from the bloodstream at a rate proportional to the amount present. The amount of glucose in grams in the bloodstream at time t (in minutes) is given by

where a is a positive constant. Assume g0 = 0.08, c = 0.1, and a = 1.3.
(a) At what time is the amount of glucose a maximum? What is the maximum amount of glucose in the bloodstream?
(b) When is the amount of glucose in the blood-stream 0.1 g?
(c) What happens to the amount of glucose in the bloodstream after a very long time?

Transcribed Image Text:

a D m 2 ( 57 - 08) + ² = (1) 8