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.

Answer with explanation:

Temperature in the living room =68°F

The 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 function

Z= A cos (sx+q)+r

As period of cos x is 2 π.

So,the given function has period

So, the period of function 1, is given by

⇒The meaning of period of the function is that after every period of   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 ≤ 1

So, the Maximum value of function = 2 ×1+68°=70°----Maximum Temperature

And, the minimum value of function = 2 ×(- 1)+68°=66°----Minimum Temperature

a negative exponent is translated as follows:

so, we have

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