a) The period of the function y = H(t) is 10 hours, the midline is 62.5°C, and the amplitude is 52.5°C.
b) The midline is the average of the lowest temperature (10°C) and the highest temperature (115°C), which is 62.5°C.
c) The amplitude of the function y = H(t) is = 52.5°C.
(a) The period of the function y = H(t) represents the time it takes for the function to complete one full cycle.
In this case, the temperature oscillates between a low of 10°C and a high of 115°C, and it takes the same amount of time to go from the highest point to the lowest point and back to the initial temperature.
Therefore, the period is 10 hours, which is the total time it takes for the temperature to complete one cycle.
(b) The midline of the function y = H(t) represents the average temperature of the reaction.
In this case, the midline is the average of the lowest temperature (10°C) and the highest temperature (115°C), which is (10+115)/2 = 62.5°C.
(c) The amplitude of the function y = H(t) represents half the distance between the highest and lowest points of the temperature oscillation.
In this case, the amplitude is (115-10)/2 = 52.5°C.
The probable question may be:
The temperature of a chemical reaction oscillates between a low of 10 °C and a high of 115 °C. The temperature is at its highest point at 0, and reaches its minimum point over a five-hour period. It then takes the same amount of time to return back to its initial temperature. Let y = H(t) denote the temperature of the reaction t hours after the reaction begins.
(a) What is the period of the function y = H(t)? _______ Include units in your answer.
(b) What is the midline of the function y = H(t)? y =_____ Include units in your answer
(c) What is the amplitude of the function y = H(t)?________ Include units in your answer