Suppose that a liquid carries a drug into a 400-cc organ at a rate of 20 cc/s and leaves the organ at the same rate. Suppose that the concentration of the drug entering is 0.25 g/cc. Find the amount A of drug in the organ as a function of time t if initially there is none in the organ. If it's necessary, round your calculations to four decimal places.

Question

Suppose that a liquid carries a drug into a 400-cc organ at a rate of 20 cc/s and leaves the organ at the same rate. Suppose that the concentration of the drug entering is 0.25 g/cc. Find the amount A of drug in the organ as a function of time t if initially there is none in the organ. If it's necessary, round your calculations to four decimal places. ​

Quizplus · Accepted Answer

The amount of drug in the organ can be found using the formula:

A = (concentration of drug in liquid * volume of liquid that enters per second - concentration of drug in organ * volume of liquid that leaves per second) * t

At time t = 0, there is no drug in the organ, so the initial concentration of drug in the organ is 0 g/cc.

Substituting the given values, we get:

A = (0.25 * 20 - 0 * 20) * t
A = 5t

Therefore, the amount of drug in the organ as a function of time is A = 5t.

At t = 80 seconds (when 400 cc of liquid has entered and left the organ), the amount of drug in the organ will be:

A = 5 * 80
A = 400

Therefore, the amount of drug in the organ at any time t is 5t, which means that the drug accumulates linearly in the organ over time. The closest answer choice is B).

Suppose That a Liquid Carries a Drug into a 400-Cc