Project A01 - It's a Hot One

A new fever-reducing drug has the effect of lowering a patient's body temperature from T0 (102°F £ T0 £ 105°F) to
T(t) = T0 - 24t
(2t+1)2
where T is measured in degrees Fahrenheit and t is the number of hours after the drug is administered.

Suppose that a patient's initial body temperature is 104.8°F.

  1. Sketch the graph of T on the interval [0,8].
  2. Explain why the model described above makes sense.
  3. What do you notice about the slope of the line tangent to the graph of T at the point where T attains its minimum value?
  4. Determine the derivative of T(t).
  5. How many hours after the drug is administered will the body temperature be at a minimum? What is that minimum temperature?
  6. Suppose that after receiving a first dose of the drug, a second dose must be administered when the patient's body temperature rises to 103°F. When should the second dose be administered? Round your result to the nearest minute.
  7. Assuming a second dose is administered at the appropriate time, the patient's body temperature after t hours (0 £ t £ 8) is shown in the following graph.
    Explain. (Notice that some of the drug from the first dose still remain in the patient's bloodstream after the second dose is given.)
  8. Assuming a second dose is administered at the appropriate time, what will the patient's body temperature be 4 hours after the first dose is given? Round your result to the nearest tenth of a degree.

File translated from TEX by TTH, version 1.98.
On 15 Jan 2000, 14:03.