the question says: the yearbook committee is distributing yearbooks to students by class. Each class has approximately the same number of students. The table shows number of volunteers who helped to distribute the yearbooks to each of the four classes and the time needed to distribute the yearbooks. What function models the data?
Number of vollunteers
2 5 8 11
time in minutes
220 88 55 40
nt=440
Well, this seems like a simple case of "More Volunteers, Less Time!" So I would say the function that models this data is probably an inverse function. As the number of volunteers increases, the time needed to distribute the yearbooks decreases. So the function could be something like:
Time = f(Volunteers)
Where f(Volunteers) is an inverse relationship. But I must say, it's quite impressive to see the time drop from 220 minutes to just 40 minutes with more volunteers. Looks like those yearbook distributions were a well-oiled machine!
To determine the function that models the data, we can analyze the relationship between the number of volunteers and the time needed to distribute the yearbooks.
We can observe that as the number of volunteers increases, the time needed to distribute the yearbooks decreases. This suggests an inverse relationship between the variables.
To find the equation of the function, we can create a scatter plot using the given data points:
(Number of volunteers, Time in minutes)
(2, 220)
(5, 88)
(8, 55)
(11, 40)
Next, we can determine the equation of the line that best fits the data points. This can be done by finding the equation of the line in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
To find the slope (m), we can use the formula:
\(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\)
Let's select the first two data points (2, 220) and (5, 88) to calculate the slope:
\(m = \frac{{88 - 220}}{{5 - 2}} = -44\)
Now that we have the slope, we can substitute one of the data points (let's use the first point - 2, 220) into the slope-intercept form equation to find the y-intercept (b):
\(220 = -44(2) + b\)
\(220 = -88 + b\)
\(b = 308\)
Therefore, the equation of the function that models the data is:
\(y = -44x + 308\)
where y represents the time in minutes and x represents the number of volunteers.
To determine the function that models the data, we should look for a relationship between the number of volunteers and the time needed to distribute the yearbooks. We can start by creating a graph with the number of volunteers on the x-axis and the time in minutes on the y-axis.
Plotting the given data points, we have the following coordinates:
(2, 220), (5, 88), (8, 55), (11, 40)
Visually, it appears that there is a negative correlation between the number of volunteers and the time needed. As the number of volunteers increases, the time needed to distribute the yearbooks decreases.
To find the relationship more precisely, we can try fitting a linear function to the data points. A linear function has the form y = mx + b, where m is the slope and b is the y-intercept.
Using the two points (2, 220) and (11, 40), we can find the slope:
m = (y2 - y1) / (x2 - x1)
= (40 - 220) / (11 - 2)
= -180 / 9
= -20
Now, let's find the y-intercept:
Using the point (2, 220) and the slope m = -20:
220 = -20(2) + b
220 = -40 + b
b = 260
Therefore, the linear function that models the data is:
time in minutes = -20(number of volunteers) + 260
This function shows that for every additional volunteer, the time needed to distribute the yearbooks decreases by 20 minutes.