ADVANCED EXERCISES - Modeling 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?

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(2) The Bay of Fundy is reported to have the largest tides in the world, with the difference between low and high level being as much as 15 meters. Suppose at a particular point in the Bay of Fundy, the depth of the water, y, in meters, as a function of time, t, in hours, from midnight on January 1, 1994, is given by

y = y0 + a cos[b(t - t0)].
  1. What is the physical meaning of y0?
  2. What is the value of a?
  3. What is the value of b? Assume the time between successive high tides is 12.5 hours.
  4. What is the physical meaning of t0?


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