A 154lb person burns 420 calories per hour riding a exercise bicycle at a rate of 15 mi/hr. Can you explain how to write a function to represent the total calories burned over time by that person. Explain how the information in the problem relates to the function
To write a function that represents the total calories burned over time by the person, we first need to understand the relationship between the calories burned and time.
From the information given in the problem, we know that the person burns 420 calories per hour of riding the exercise bicycle. This means that the rate of calories burned is constant at 420 calories per hour.
We also know that the person is riding the exercise bicycle at a rate of 15 miles per hour. However, the problem does not provide any information about how this relates to the calories burned. Therefore, we cannot directly incorporate the rate of 15 miles per hour into the function.
Given these considerations, we can write the function as follows:
Let T represent the total time in hours.
The function, f(T), that represents the total calories burned over time is:
f(T) = 420 * T
Here, 420 represents the calories burned per hour and T represents the total time in hours. Multiplying the rate of calories burned per hour (420) by the total time in hours will give us the total calories burned over that time.
For example, if the person rides the exercise bicycle for 2 hours, we can calculate the total calories burned as:
f(2) = 420 * 2 = 840 calories.
Therefore, the function f(T) = 420 * T represents the total calories burned over time by the person.
I understand more on how to write the function rule but I still don't understand how the information in the problem relates to the function can you clarify a little further?
Certainly!
The information provided in the problem - that a 154lb person burns 420 calories per hour riding an exercise bicycle at a rate of 15 mi/hr - directly relates to the function we wrote.
The problem states that the person burns 420 calories per hour of riding the exercise bicycle. This means that for every hour the person rides the bicycle, they burn 420 calories. In terms of our function, this is exactly what we wrote:
f(T) = 420 * T
Here, T represents the total time in hours. So, if the person rides the bicycle for 1 hour (T = 1), the function tells us that they will burn 420 * 1 = 420 calories. Similarly, if they ride for 2 hours (T = 2), the function tells us that they will burn 420 * 2 = 840 calories.
The rate of riding the exercise bicycle, which was given as 15 miles per hour, does not directly affect the function or the total calories burned. It may be used to calculate the total distance traveled over time, but it is not necessary to determine the total calories burned in this problem.
In summary, the information in the problem directly relates to the function by providing the rate at which calories are burned per hour (420 calories), which we used to calculate the total calories burned over time by multiplying this rate by the total time in hours (T).