A 145-lb person burns 420 calories per hour ridding an exercise bicycle at a rate of 15 mi/he write a function rule to represent the total calories but 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 a 145-lb person riding an exercise bicycle at a rate of 15 mi/hour is:
C(t) = 420t
where C represents the total calories burned and t represents the time in hours.
The information in the problem provides us with two important pieces of information for this function rule: the person's weight (145 lbs) and the rate at which they are cycling (15 mi/hour). These two pieces of information allow us to calculate the number of calories burned per hour (420 calories/hour) using a formula such as the one provided by the American Council on Exercise:
Calories Burned Per Minute = (0.175 x Body Weight in Pounds) x MET x Duration in Minutes / 60
where MET is the metabolic equivalent of the activity, which for cycling at a moderate pace (10-12 miles/hour) is approximately 6.0. Using this formula, we can calculate that a 145-lb person cycling at a rate of 15 mi/hour burns approximately 7.2 calories per minute or 420 calories per hour.
The function rule C(t) = 420t allows us to calculate the total number of calories burned over any period of time t in hours. For example, if the person cycles for 30 minutes, we can calculate the total number of calories burned as follows:
C(0.5) = 420 x 0.5 = 210
Therefore, the person would burn approximately 210 calories in 30 minutes of cycling at a rate of 15 mi/hour.
The function rule to represent the total calories burned over time can be defined as follows:
Let "c" be the total calories burned over time (in calories).
Let "t" be the time spent exercising (in hours).
Based on the given information, we know that a person burns 420 calories per hour riding an exercise bicycle. Additionally, the person rides the bicycle at a rate of 15 miles per hour.
To calculate the total calories burned over time, we can use the following formula:
c = 420 * t
In this formula, the calories burned per hour (420) is multiplied by the time spent exercising (t). This gives us the total calories burned over time (c).
This function rule directly relates the time spent exercising to the total calories burned, taking into account the rate at which the person rides the exercise bicycle.