UCSS Math III 4B.1.2 Example 2

Certain medical tests require that patients be injected with liquids containing trace amounts of radioactive elements in order to track the movement of blood in the circulatory system. The concentration of the radioactive tracer substance diminishes in the human body over time according to the function , in which is a constant unique to the tracer , is time in hours, and is the concentration of the tracer in milligrams per liter. Identify real-world and mathematical constraints on , the time that the tracer is in the body, which allow to be defined in the context of the situation.
  1. Identify a real-world condition that might be placed on the time variable, .
  2. Determine any specific mathematical constraints on .
  3. Use the quadratic formula to find value(s) of for which the denominator is nonzero.
  4. Find the initial concentration of the radioactive tracer at .
  5. Combine the results of the previous steps to determine a realistic domain for the time in this problem.
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