Q:

Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. Determine the period of the function and explain what it represents. Include the maximum and minimum temperatures in your answer.

Accepted Solution

A:
Answer with explanation:Temperature in the living room =68°FThe equation which satisfies ,the  room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies  t=2 Cos (0.21 m) +68----------(1)⇒To determine the period of the functionZ= A cos (sx+q)+rAs period of cos x is 2 π.So,the given function has period         [tex]=\frac{2\pi}{s}[/tex]            So, the period of function 1, is given by         [tex]=\frac{2\pi}{0.21}[/tex]   ⇒The meaning of period of the function is that after every period of   [tex]=\frac{2\pi}{0.21}[/tex] the temperature of the room increases or decreases by an integer equal to 2.⇒Cosine function has maximum value of 1 , and Minimum value of -1.-1 ≤ Cos x ≤ 1So, the Maximum value of function = 2 ×1+68°=70°----Maximum TemperatureAnd, the minimum value of function = 2 ×(- 1)+68°=66°----Minimum Temperature