Felicity set the thermostat of her refrigerator to 37°F. The refrigerator temperature t in degrees Fahrenheit h hours after the temperature sensor in the refrigerator is activated satisfies t=1cos (1.05h) + 37. Determine the period of the function and explain what it represents. Include the maximum and minimum temperatures in your answer.

6

Step-by-step explanation:

Felicity set the thermostat of her refrigerator to 37°F. The refrigerator temperature t in degrees Fahrenheit h hours after the temperature sensor in the refrigerator is activated satisfies t=1cos (1.05h) + 37. Therefore, the period of the function is 6.

Period=6

Step-by-step explanation:

Given:

t=1cos (1.05h) + 37

Using acos (bx-c) + d to find the period of the given function

amplitude = a

period = 2π/Bb

phase shift=c (positive is to the left)

vertical shift=d

comparing with t=1cos (1.05h) + 37, we get

a=1

b=1.05

c=0

d=37

period = 2π/b

=2π/1.05

=5.983

=6

Period of function is 6, after every 6 hours the refrigerator sensor will reach its maximum temperature and the cycle will move towards reducing temperature i. e it'll reach the minimum temperature then again the cycle will move upwards raising the temperature to maximum and so one period will be completed!