A Drug Is Administered to a Patient and the Concentration $c$

question 128

Essay

A drug is administered to a patient and the concentration $c$ of the drug in the bloodstream is monitored. At the time $t \geq 0$ (in minutes since the injection), the concentration (in mg/L) is given by $c ( t ) = \frac { 55 t } { t ^ { 2 } + 3 }$ .
(a) Draw a graph of the drug concentration.
(b) What eventually happens to the concentration of the drug in the bloodstream?
(c) What is the highest concentration of the drug that is reached in the patient's bloodstream? When does this occur?

---

Definitions:

Total Costs

The aggregate of all financial outlays involved in the creation of goods or services, covering both stable and changeable costs.

Public Good

A commodity or service that is provided without profit to all members of a society, either by the government or a private individual or organization.

Free-Rider Problem

The inability of potential providers of an economically desirable good or service to obtain payment from those who benefit, because of nonexcludability.

Highly Profitable

Describing a business or activity that generates a significantly higher amount of earnings compared to its costs.