Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C(t) = −2t^2 + 8t, where the time, t, is hours after injection.

Question

Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C(t) = −2t^2 + 8t, where the time, t, is hours after injection.

Part A: What are the domain and range of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points)

Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)

Answer 1

Part A:

Domain: t ≥ 0
Range: C ≥ 0

Part B:
The graph of the function C(t) is a parabola that opens downward. The greatest concentration of the medication that a patient will have in their body is 8 mg/L, which occurs when t = 4 hours after injection.