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 of t is equal to the quantity negative 18 times t squared plus 54 times t end quantity over the quantity t squared plus 7 times t plus 10 end quantity comma 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. (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

The domain of the function is 0 ≤ t ≤ 3 and the greatest concentration of the medication is 2mg/L

The domain of the function

The equation of the function is given as:

$C(t) = \frac{-18t^2 + 54t}{t^2 + 7t + 10}$

Time can be 0 or greater but cannot be negative.

So, the domain of the function includes t ≥ 0

Set the function to 0 to determine the maximum value of t.

$\frac{-18t^2 + 54t}{t^2 + 7t + 10} = 0$

Cross multiply

$-18t^2 + 54t = 0$

Factor out -18t

-18t(t - 3) = 0

Divide both sides by -18t

t - 3 = 0

Add 3 to both sides

t = 3

This means that the maximum value of t is 3

Hence, the domain of the function is 0 ≤ t ≤ 3

The greatest concentration of the medication

From the graph of the function (see attachment), we have the maximum value to be;

C(t) = 2

Hence, the greatest concentration of the medication is 2mg/L

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brainly.com/question/1214333

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