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.
Simple answer
Function rule: C(t) = 420t, where t is the time in hours and C(t) is the total number of calories burned by the person in t hours.
Explanation: The given information provides us with the rate at which the person burns calories on the exercise bicycle, which is 420 calories per hour. This rate is constant and can be represented as the slope of a linear function. The function rule C(t) = 420t reflects this linear relationship between the number of calories burned and the time spent exercising. The input t (time) is multiplied by the rate (420 calories/hour) to get the output C(t) (total calories burned). Thus, the function gives us a way to predict the total number of calories that a 154-lb person will burn over any given period of time while riding an exercise bicycle at a rate of 15 mi/hr.
The function rule to represent the total calories burned over time can be written as:
Calories burned = (Calories burned per hour) x (Time in hours)
In this case, the person burns 420 calories per hour riding an exercise bicycle. So the function rule becomes:
Calories burned = 420 x Time
This equation shows that the total calories burned depends on the time the person spends riding the exercise bicycle. The longer the person rides, the more calories are burned.