Question

Select the correct answer.
Sully is a vocalist in a rock band. The table provided shows the number of tracks his band records and the respective number of albums consisting of those recordings.

Number of Albums Number of Tracks
2 16
4 32
6 48
8 64
10 80

What is the rate of change of the number of tracks Sully’s band records with respect to each album the band releases?
A.
2 tracks per album
B.
8 tracks per album
C.
17 tracks per album
D.
6 tracks per album

Answer 1

To find the rate of change of the number of tracks with respect to each album, we can look at the relationship between the number of tracks and the number of albums:

From the table:
- For 2 albums, there are 16 tracks.
- For 4 albums, there are 32 tracks.
- For 6 albums, there are 48 tracks.
- For 8 albums, there are 64 tracks.
- For 10 albums, there are 80 tracks.

We can determine that for every 2 additional albums, there are 16 additional tracks.

To calculate the rate of change, we can take any two points (for example, using the first and last data points):

1. The first point is (2 albums, 16 tracks).
2. The last point is (10 albums, 80 tracks).

The change in the number of albums = 10 - 2 = 8 albums.

The change in the number of tracks = 80 - 16 = 64 tracks.

Now, we can calculate the rate of change:

\[
\text{Rate of change} = \frac{\text{Change in Tracks}}{\text{Change in Albums}} = \frac{64 \text{ tracks}}{8 \text{ albums}} = 8 \text{ tracks per album}.
\]

Thus, the correct answer is **B. 8 tracks per album.**