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.
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
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