Question

Help please :)))))))

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) = −3t2 + 12t, 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, and the time when that occurs. (5 points)

Answer 1

The domain is t ≥ 0

The range is 0 ≤ y ≤ 12

Part B. The greatest concentration is 12 mg/L and the time is 2 hours

How to find the domain and range

To determine the domain and range of the function C(t) = -3t² + 12t we consider the problem

In this problem, time cannot be negative, hence the domain is t ≥ 0

The range of a function, from the graph, the maximum value, which is at the vertex shows y = 12, the minimum value when the domain is zero is still zero. The graph passed through the origin, hence the range is

0 ≤ y ≤ 12

Pert B. The greatest concentration is at the vertex (2, 12). This is at 12 mg/L at 2 hours