Answer:
The temperature at 9AM = 75°F
Step-by-step explanation:
Consider D(t) be the temperature in Fahrenheit at time t, where t is measured in hours since midnight. It knows when the maximum temperature occurs. Then it can create a model using a cosine curve.
Vertical shift, D = 85°F
Amplitude, A = (105-85)°F = 20°F
Horizontal stretch factor, B = 2π/24 = π/12
Horizontal shift = -(12+5) = -17
Using the information, we have this model
D(t) = 20cos [π/12(t-17)] + 85
D(9) = 20cos [π/12(9-17)] + 85
= 20cos [-2π/3] + 85
= -20 x 1/2 + 85
= 75°
