What is the rate of change of the number of tracks Sully's band records with respect to each album the band releases, given the following data: Number of Albums Number of Tracks 2... What is the rate of change of the number of tracks Sully's band records with respect to each album the band releases, given the following data: Number of Albums Number of Tracks 2 16 4 32 6 48 8 64 10 80
Understand the Problem
The question asks us to determine the rate of change (tracks per album) from a table showing the number of albums and tracks. This is a linear relationship, and the rate of change is the slope of the line represented by the data.
Answer
12 tracks per album
Answer for screen readers
The rate of change is 12 tracks per album.
Steps to Solve
- Choose two points from the table
We need to select two points from the table to calculate the slope. Let's choose the points (1, 12) and (3, 36). These represent (albums, tracks).
- Apply the slope formula
The slope formula is:
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
Where $m$ is the slope, $(x_1, y_1)$ and $(x_2, y_2)$ are the two points.
- Substitute the values into the slope formula
Substitute the coordinates of our chosen points (1, 12) and (3, 36) into the slope formula:
$$m = \frac{36 - 12}{3 - 1}$$
- Simplify the equation
Simplify the numerator and denominator:
$$m = \frac{24}{2}$$
- Calculate the slope
Divide to find the slope:
$$m = 12$$
The rate of change is 12 tracks per album.
The rate of change is 12 tracks per album.
More Information
The rate of change represents the number of tracks added for each additional album. In this case, for every album, there are 12 tracks.
Tips
A common mistake is to reverse the order of subtraction in the numerator or denominator, leading to a negative slope or an incorrect positive slope. Another mistake could be incorrectly reading data from the table. Ensure the y values correspond to the correct x values.
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