Question

the concentration of a drug (in parts per million) in a patients bloodstream t hours after administration of the drug is given by the function p(t)= -t^4 + 12t^3 - 58t^2 + 132t. the corresponding graph is shown to the right. complete parts a through d.
a. use the formula to determine when the drug will be totally eliminated from the bloodstream.
the drug will be totally eliminated from the bloodstream in 6 hours.
(simplify your answer.)
b. use the graph to estimate the maximum concentration of the drug.
the maximum concentration of the drug is about 110 ppm.
(round to the nearest integer as needed.)
c. use the graph to estimate the time at which the maximum concentration occurs.
the maximum concentration occurs approximately hours after administration of the drug.

Explanation:

Step1: Analyze the graph

By observing the graph, we can see the peak of the curve which represents the maximum - concentration point.

Step2: Estimate the time

The x - coordinate of the peak of the curve gives the time at which the maximum concentration occurs. Looking at the graph, the maximum concentration occurs approximately 3 hours after administration of the drug.

Answer:

3