Question

An oral painkiller is administered to a patient, and t hours later, the concentration of the drug in the patient's bloodstream is given by C(t) = 2t/3t2+16. a. Use the quotient rule to find the rate at which the concentration of the drug in the patient's bloodstream is changing t hours after being administered? b. At what rate is the concentration of the drug changing after 1 hour? Is the concentration increasing or decreasing at this time? c. When does the concentration of the drug begin to decline?​

Answer 1

Answer:

sorry I didn't understand

Answer 2

Given: An oral painkiller is administered to a patient, and t hours later, the concentration of the drug in the patient's bloodstream is given by C(t) = 2t/3t2+16.

To find:

a. Use the quotient rule to find the rate at which the concentration of the drug in the patient's bloodstream is changing t hours after being administered?

b. At what rate is the concentration of the drug changing after 1 hour? Is the concentration increasing or decreasing at this time?

c. When does the concentration of the drug begin to decline?​

Solution:

a.

In order to find the rate at which the concentration of the drug in the patient's bloodstream is changing t hours after being administered can be calculated as follows.

$\frac{C(t)}{t} = \frac{2t}{3t^{2} } * \frac{1}{t} + \frac{16}{t}$

       $= \frac{2}{3t^{2} } + \frac{16}{t}$

b.

After 1 hour, the change in the concentration of the drug can be calculated as follows.

$\frac{2}{3t^{2} } + \frac{16}{t} = \frac{2}{3(1)^{2} } + \frac{16}{(1)}$

             $= 16.67 / hour$

The concentration is increasing at this time.

c.

When t is greater than 16, the value of the rate at which the concentration is increasing stops increasing and starts decreasing. Thus, after 16 hours the concentration of the drug begin to decline.

Therefore,

a. The rate at which the concentration of the drug in the patient's bloodstream is changing t hours after being administered is (2/3t²+16/t).

b. The concentration of the drug changing after 1 hour is 16.67 per hour. The concentration is increasing.

c. After 16 hours, the concentration of the drug begin to decline.