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
The function rule to represent the total calories burned over time by a 154-lb person riding an exercise bicycle at a rate of 15 mi/hr is:
C(t) = 420t
where C(t) represents the total calories burned over time (t) in hours.
Sure! Here's a function rule to represent the total calories burned over time:
Total Calories Burned = (Person's Weight in lbs * Calories Burned per Hour) / (Biking Speed in mph)
In this case, let's say the person's weight is 154 lbs and they burn 420 calories per hour while riding the exercise bicycle at a rate of 15 mph. Plugging these values into the formula, the function rule would be:
Total Calories Burned = (154 lbs * 420 calories/hr) / (15 mph)
You can simplify this further if needed.
To write a function rule to represent the total calories burned over time by a person riding an exercise bicycle, we can use the given information:
- The person weighs 154 lbs (let's convert this to kg for the equation).
- The person burns 420 calories per hour.
- The person rides the exercise bicycle at a rate of 15 miles per hour.
Let's start with converting the weight of the person from pounds to kilograms. Since 1 lb is approximately equal to 0.45 kg, we can calculate the weight in kilograms:
Weight in kg = 154 lbs * 0.45 kg/lb
Weight in kg = 69.3 kg (approximately)
Next, we need to determine the distance covered by the person in 1 hour. Using the speed and time formula (Speed = Distance / Time), we can calculate the distance:
Distance covered in 1 hour = Speed * Time
Distance covered in 1 hour = 15 miles/hr * 1 hr
Distance covered in 1 hour = 15 miles
Now, let's use the formula for calories burned while riding an exercise bicycle:
Calories burned = Weight in kg * Distance covered in 1 hour * Caloric expenditure constant
From the given information, the caloric expenditure constant is 420 calories per hour. Therefore, the function rule to represent the total calories burned over time by the person riding an exercise bicycle is:
Calories burned = 69.3 kg * 15 miles * 420 calories/hr
Calories burned = 69.3 kg * 15 miles * 420 calories/hr
Calories burned = 46,071 calories/hr (approximately)
Note that this function rule assumes a constant speed and weight throughout the entire duration of riding the exercise bicycle.
To write a function rule that represents the total calories burned over time by a person riding an exercise bicycle, we need to define the relationship between the calories burned and the duration of the exercise.
Let's start by identifying the variables involved:
C = calories burned
w = weight of the person (in pounds)
R = rate of exercise (in mph)
t = duration of exercise (in hours)
According to the given information, the person's weight is 154 pounds, the exercise rate is 15 mph, and the calorie burn rate is 420 calories per hour.
To find the total calories burned, we can use the formula:
C = (w/154) * (R/15) * 420 * t
In this formula, (w/154) represents the person's weight as a proportion of 154 pounds, (R/15) represents the exercise rate as a proportion of 15 mph, 420 represents the calorie burn rate per hour, and t represents the duration of exercise in hours.
Therefore, the function rule to represent the total calories burned over time by that person can be written as:
C(t) = (w/154) * (R/15) * 420 * t