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 3 hours after administration of the drug.
d. use the graph to estimate the amount of time for which the concentration is above 80 ppm.
the approximate amount of time for which the concentration is above 80 ppm is hour(s).
(round to the nearest integer as needed.)

Explanation:

Step1: Analyze the graph

Locate the points where the concentration - time curve intersects the 80 - ppm line.

Step2: Estimate the time interval

From the graph, the curve crosses the 80 - ppm line at approximately \(t = 1.5\) hours and \(t = 5\) hours.

Step3: Calculate the time duration

Subtract the starting time from the ending time: \(5 - 1.5=3.5\). Rounding to the nearest integer, we get 4 hours.

Answer:

4