A 154-lb person burns 420 calories per hour riding an exercise bicycle at a rate of 15 mi/hr. Write a function rule to represent the total calories burned over time by that person. Explain how the information in the problem relates to the function.
One possible function rule to represent the total calories burned over time by a 154-lb person riding an exercise bicycle at a rate of 15 mi/hr is:
C(t) = 420t
where C(t) is the total number of calories burned after t hours of riding. This function assumes that the person maintains a constant speed and resistance throughout the exercise, and that the efficiency of the machine and the body remains constant.
The information in the problem relates to the function in several ways. First, it gives us the rate at which the person burns calories per hour, which is constant and equal to 420. This tells us that for each hour of exercise, the person burns 420 calories. Second, it specifies the weight of the person as 154 lbs, which may affect the energy expenditure due to relative muscle mass, metabolism, and thermoregulation. However, this information is not directly included in the function, which only depends on the time of exercise. Finally, it states the speed of the bicycle as 15 mi/hr, which may influence the intensity and duration of the workout, but again is not explicitly incorporated into the function. Overall, the function rule captures a simplified relationship between time and total calorie burn, based on a set of assumptions and measurements.