Match the function with the graph that best describes the situation.
-The concentration C (arbitrary units) of a certain drug in a patient's bloodstream can be modeled using $$C ( t ) = \frac { t } { ( 0.423 t + 2.366 ) ^ { 2 } }$$ where t is the number of hours since a 500 milligram oral dose was administered. Using the TABLE feature of a graphing utility, find the time at which the concentration of the drug is greatest. Round
To the nearest tenth of an hour.
A) 5.6 hours
B) 6.4 hours
C) 7.1 hours
D) 7.9 hours

Question

Quizplus · Accepted Answer

To find the time at which the concentration of the drug is greatest, we need to find the maximum value of the function $C(t) = \frac{t}{(0.423t + 2.366)^2}$. This involves calculus techniques such as taking the derivative of the function and setting it equal to zero to find critical points, or using a graphing utility to directly observe the behavior of the function. By using a graphing utility and examining the table of values for $C(t)$, we can identify the time at which $C(t)$ reaches its maximum value. The correct answer, rounded to the nearest tenth of an hour, is 5.6 hours, indicating that the concentration of the drug in the bloodstream is greatest approximately 5.6 hours after administration.

Match the Function with the Graph That Best Describes the Situation