The concentration (in milligrams/cubic centimeter) of a certain drug in a patient's body t hr after injection is given by interval where N is decreasing. When is the concentration of the drug increasing and when is it decreasing?
A)Decreasing on (0, 2.5)
B)Increasing on (0, 1) and decreasing on (1, 5)
C)Increasing on (0, 10)
D)The concentration of the drug is constant.

Question

The concentration (in milligrams/cubic centimeter) of a certain drug in a patient's body t hr after injection is given by  interval where N is decreasing. When is the concentration of the drug increasing and when is it decreasing?
A)Decreasing on (0, 2.5) 
B)Increasing on (0, 1) and decreasing on (1, 5) 
C)Increasing on (0, 10) 
D)The concentration of the drug is constant.

Quizplus · Accepted Answer

The derivative of the given function is -0.45te^(-0.45t). This is positive for t<1, meaning the concentration is increasing on the interval (0, 1). The derivative is negative for t>1, meaning the concentration is decreasing on the interval (1, 5). The derivative is also always negative, indicating that the concentration is always decreasing, ruling out choices C and D. Therefore, the concentration is decreasing on (0, 2.5) and increasing on (0, 1) and decreasing on (1, 5), making choice B the best choice.

The Concentration (In Milligrams/cubic Centimeter) of a Certain Drug in a Patient's