Final answer:
The amplitude of the temperature variation in the model T = 50 + 10sin[π(t - 8)] is 10 degrees Fahrenheit.
Step-by-step explanation:
The mathematical model given for temperature variation is T = 50 + 10sin[π(t - 8)]. The amplitude of a sinusoidal function is the coefficient before the sine or cosine function, which dictates the maximum deviation from the function's mean value. In this case, the coefficient before the sine function is 10, representing the amplitude of the temperature variation.
Therefore, the amplitude of the temperature variation in the given model is 10 degrees Fahrenheit.The amplitude of a wave is the maximum displacement from the equilibrium position. In the given mathematical model T = 50 + 10sin[π(t - 8)], the coefficient of the sine function, 10, represents the amplitude of the temperature variation.Therefore, the amplitude of the temperature variation is 10 degrees Fahrenheit (option a).