ADVANCED EXERCISES-Modelling with Trigonometric Functions

(1) A patient in the hospital had an illness in which his temperature (in degrees Celsius) varied from a low of 37o to a high of 40.4o. The length of time between successive highs is 16 days.

  1. Determine the formula for the temperature, T, of the patient at time t in days since the beginning of the illness. Assume that the function describing the temperature can be modeled with a sine function, with no phase shift.
  2. Sketch a graph of the function over the interval 0 t 20.
  3. According to this model, what was the patient's original temperature?
  4. What is the patient's temperature on day 4 of his illness?
  5. When does the first temperature high occur? 

SOLUTION:

(a) T(t) = 38.7 + 1.7[sin(t/8)]

(b) 


(c) The patient's original temperature was 38.7oC

(d) The temperature when t = 4 days is 40.4oC

(e) The first temperature high occurs when t = 4 days




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