Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response to 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 8 times t squared plus 56 times t end quantity over the quantity t squared plus 3 times t plus 2 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)

When a function is plotted on a graph, the domain and the range of the function are the x-coordinate and the y-coordinate respectively.

Given that:

To calculate the domain, we start by equating the denominator to 0

Expand

Factorize

Factor out t + 1

Split

or

Solve for t

This means that the values of t cannot be -1 and -2.

Since t represents the hours after injection, the value of t cannot be negative.

Hence, the domain of the function is:

See attachment for the graph of

From the attachment, we can see that the maximum of the function on the y-axis is 8.

This means that the greatest concentration of medication that a patient will have in their body is 8mg/L

Read more about domains and equations at:

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step-by-step explanation: