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.
Let x be the number of hours of exercise biking.
The function rule to represent the total calories burned over time by that person is:
C(x) = 420x
This function represents a linear relationship between the number of hours spent biking and the total number of calories burned. The slope of the line is 420, which represents the rate of calorie burning per hour. The y-intercept of this line is 0, which makes sense since if the person doesn't bike at all (x = 0), then no calories are burned.
The given information in the problem (the weight of the person and the rate of biking) is used to calculate the rate of calorie burning per hour, which is then used as the slope of the function. The independent variable is the number of hours spent biking, while the dependent variable is the total number of calories burned.
To write a function rule that represents the total calories burned over time by the person, we can use the formula:
Calories burned = (Calories burned per hour) x (Number of hours)
In this case, the person burns 420 calories per hour and the information in the problem says that the person rides the bicycle at a rate of 15 mi/hr. To relate this information to the function, we need to determine the number of hours spent riding the bicycle.
We can use the formula:
Number of hours = (Total distance) / (Rate)
In this case, the total distance is not given, but we have the rate (15 mi/hr) and the weight of the person (154 lbs). To find the total distance, we can use the formula:
Total distance = (Rate) x (Time)
Therefore, the function rule that represents the total calories burned over time by the person is:
Calories burned = 420 x [(Rate x Time) / (Rate)]
Simplifying this expression, we get:
Calories burned = 420 x Time
So, the function rule is:
Calories burned = 420(T)
Where T represents the number of hours spent riding the exercise bicycle.