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Chapter 4: Q. 49 (page 235)

The concentration C of a certain drug in a patient's bloodstream t hours after injection is given by

Ct=t2t2+1

Part (a): Find the horizontal asymptote of Ct. What happens to the concentration of the drug as t increases?

Part (b): Using your graphing utility, graph C=Ct.

Part (c): Determine the time at which the concentration is highest.

Short Answer

Expert verified

Part (a): The horizontal asymptote of Ct is t-axis.

When t increases, the concentration of the drug is givenCt鈫�0.

Part (b): On plotting the graph, we get,

Part (c): Concentration is highest at 0.71hours after injection.

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given function,

Ct=t2t2+1

The horizontal of this function can be given by,

localid="1646069009980" =limx鈫�鈭�C(t)

Using the long division method,

localid="1646069014524" =limx鈫�鈭�12t+1t

We have the horizontal asymptote of the given function as y=0as x鈫�鈭�.

02

Part (b) Step 1. Plot the graph.

Plot the function C=Ct,

03

Part (c) Step 1. Determine the time.

Consider the given function,

Ct=t2t2+1

From the graph, it can be said that the concentration of the drug is highest at the time 0.71hours after injection is0.35.

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