A 154-1b 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.
The function rule to represent the total calories burned over time by that person is C(t) = 420t, where t is the number of hours the person rides the exercise bicycle. This is because the person burns 420 calories per hour, and the total calories burned is simply the product of the number of hours and the calories burned per hour.
The information in the problem provides us with two pieces of information: the person's weight (154 lbs) and the rate at which they are riding the exercise bicycle (15 mi/hr). While these pieces of information are not directly used in the function rule, they can be useful in understanding the context of the problem and in interpreting the output of the function. For example, knowing the person's weight can help us estimate their overall level of fitness, and knowing the rate at which they are riding the exercise bicycle can help us estimate the intensity of their workout.
To write a function rule that represents the total calories burned over time by the person, we need to consider that the person burns 420 calories per hour while riding the exercise bicycle at a rate of 15 mi/hr.
Let's denote the total calories burned by "C" and the time taken by "t" hours. We want to find a relation between these variables.
The information in the problem tells us that the person burns 420 calories per hour. This means that for every hour, 420 calories are burned. So, the number of calories burned is directly proportional to the number of hours.
The information also specifies that the person is riding the bicycle at a rate of 15 mi/hr. Although this information seems irrelevant to the function rule itself, it provides context for how the calories burned are affected by the exercise intensity of the person.
Therefore, the function rule can be written as:
C(t) = 420t
This function rule states that the total calories burned, C, is equal to 420 times the number of hours, t.
To write a function rule that represents the total calories burned over time by a person, we need to identify the variables and their relationship in the problem.
Let's break down the information given:
- A person who weighs 154-1b is burning 420 calories per hour.
- They are riding an exercise bicycle at a rate of 15 mi/hr.
From this information, we can identify the following variables:
- Weight of the person: 154-1b (which we can use as a constant value)
- Calories burned per hour: 420
- Velocity (rate) of riding the exercise bicycle: 15 mi/hr
- Time (in hours)
Now, let's establish the relationship between these variables:
The number of calories burned is directly proportional to the weight, the rate of riding the bicycle, and the time. In other words, the more the person weighs, the faster they ride, or the longer they ride, the more calories they will burn.
To write a function rule that represents the total calories burned over time, we can use the formula:
Total calories burned = (Calories burned per hour) * (Time in hours)
As a function, the rule looks like this:
C(t) = 420t
Where:
- C(t) represents the total calories burned over time (t)
- 420 represents the calories burned per hour
- t represents the time in hours
This function rule allows us to calculate the total calories burned for any given amount of time, given that the weight and rate of riding the exercise bicycle remain constant.