A 175-lb person burns 485 calories per hour riding an exercise bicycle at a rate of 18 mi/hr. Write a function rule to represent the total calories burned, y, over time, x, by that person. Explain how the information in the problem relates to the function.
The function rule to represent the total calories burned, y, over time, x, by that person is:
y = 485 * x
where x is the number of hours spent riding an exercise bicycle at a rate of 18 mi/hr.
The information in the problem states that the person weighs 175 lbs and burns 485 calories per hour while riding the exercise bicycle at a rate of 18 mi/hr. This information is used in the function rule to calculate the total calories burned over time. For example, if the person rides the exercise bicycle for 2 hours, the total calories burned would be:
y = 485 * 2 = 970
Therefore, the person would burn 970 calories in total over the 2-hour period.
To write the function rule that represents the total calories burned, we need to consider the rate at which calories are burned and the time elapsed.
Let's break down the information given in the problem:
- A person weighing 175 lbs burns 485 calories per hour.
- The person is riding an exercise bicycle at a rate of 18 miles per hour.
Based on this information, we can establish the following relationship between the variables:
- The rate at which calories are burned is constant at 485 calories per hour.
- The time elapsed in hours (x) and the distance traveled at a rate of 18 miles per hour are directly proportional.
Now, let's write the function rule to represent the total calories burned, y, over time, x:
y = 485x
In this function, y represents the total calories burned, and x represents the time in hours. The constant 485 is the rate at which calories are burned per hour.
The function rule states that the total calories burned (y) is equal to the rate at which calories are burned per hour (485) multiplied by the time elapsed (x) in hours.
This function describes how the total calories burned varies with the time elapsed, based on the given information about the person's weight, rate of cycling, and calories burned per hour.