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. explain how the Informacion in the problem relates in the function.
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 can be written as:
C(t) = 420t
where C(t) represents the total calories burned and t represents the time (in hours) that the person rides the exercise bicycle.
The information given in the problem, such as the person's weight, the rate of riding the exercise bicycle, and the calories burned per hour, is used to determine the constant rate of burning calories, which is 420 calories per hour. This information is then used to create a linear relationship between the time spent riding the exercise bicycle and the total calories burned. As the person rides the exercise bicycle for longer periods of time, the total calories burned will increase at a constant rate of 420 calories per hour.
Hey bot Explane how to write a untion rule from the table below then write a function rule
X 0 2 4 6
Y 2 1 0 -1
To write a function rule from the table, we need to identify the relationship between the values in the X column and the corresponding values in the Y column. We can see that as the values in the X column increase by 2, the values in the Y column decrease by 1. This tells us that the function is linear and has a slope of -1/2 (since for every increase of 2 in X, Y decreases by 1).
To write the function rule, we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope, and b is the y-intercept (the value of y when x = 0).
We already know that the slope is -1/2, so we just need to find the y-intercept. We can do this by plugging in one of the points from the table (let's use 0,2) and solving for b:
2 = (-1/2)(0) + b
b = 2
So the function rule is:
y = -1/2x + 2
Note that we can also write the function using function notation:
f(x) = -1/2x + 2
To write a function rule that represents the total calories burned over time, we need to analyze and understand the information given in the problem.
The problem provides two pieces of relevant information:
1. A 154-lb person burns 420 calories per hour while riding an exercise bicycle.
2. The person is riding the exercise bicycle at a rate of 15 miles per hour.
The first step is to understand the relationship between calories burned and time spent exercising. From the problem statement, we know that the person burns 420 calories per hour. This means that for every hour of exercise, 420 calories are burned.
The second step is to understand the relationship between time spent exercising and the distance covered on the exercise bicycle. We are told that the person is riding at a rate of 15 miles per hour. This means that for every hour of exercise, the person covers a distance of 15 miles.
Now, we can write the function rule to represent the total calories burned over time. Let's use "T" to represent the total time in hours:
Calories burned = 420 calories per hour × T hours
However, we know that for every hour of exercise, the person covers a distance of 15 miles. So, we can write:
T hours = Distance covered / Rate of exercise
Substituting this back into the previous equation, we get:
Calories burned = 420 calories per hour × (Distance covered / Rate of exercise)
Since the rate of exercise is given as 15 miles per hour, we can substitute it in:
Calories burned = 420 calories per hour × (Distance covered / 15 miles per hour)
Simplifying further, we have:
Calories burned = 28 calories per mile × Distance covered
Therefore, the function rule to represent the total calories burned over time is:
Calories burned = 28 × Distance covered
Please note that the distance covered can be measured in miles, and the calories burned will be calculated accordingly.