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 G(t) = (- 8t ^ 2 + 56t)/(t ^ 2 + 3t + 2) where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body.

Answer 1

Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.

The domain of the function is t ≥ 0

The greatest concentration of the medication is 5mg/L

Given that:

C(t) = $\frac{-8t^2 + 56t}{t^2 +3t + 2}$

(a): The domain of the function

Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.

t, cannot take negative values (i.e. it is not possible to have a negative time).

The least possible value of t is 0

So, the domain of the function based on the context is: t ≥ 0

(b) The greatest concentration of the medication

From the graph (see attachment), the maximum y-value is 5.

Hence, the greatest concentration of the medication is 5 mg/L

Learn more about functions and graphs here:

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