A study on the circadian rhythms of patients with Alzheimer’s disease found that the body temperature of patients could be described by a function of the form

where t is the time in hours since midnight. For the patients without Alzheimer’s, the average values of T₀ (the MESOR), a (the amplitude), and k (the acrophase) were 36.91°C, 0.32°C, and 14.92 hours, while for the patients with the disease, the values were 37.29°C, 0.46°C, and 16.37 hours.

(a) Graph the functions giving the temperature for each of the two groups using a graphing calculator. Do these two functions ever cross?

(b) At what time is the temperature highest for the patients without Alzheimer’s? 

(c) At what time is the temperature highest for the patients with Alzheimer’s?

Transcribed Image Text:

T = To a cos (2π(tk) 24 ·K)).