The constant of proportionality is 0.38, indicating that the total cost varies directly with the number of songs, and the relationship is given by the equation "total cost equals 0.38 times the number of songs."
To determine the constant of proportionality between the total cost and the number of songs, we can use the formula for direct variation, which is expressed as "y equals kx," where y is the dependent variable (total cost), x is the independent variable (number of songs), and k is the constant of proportionality.
From the given data:
When there are 3 songs, the total cost is $1.14.
When there are 12 songs, the total cost is $4.56.
When there are 16 songs, the total cost is $6.08.
Let's use the first set of data (3 songs, $1.14) to find k:
1.14 equals 3k
Solving for k:
k equals 1.14 divided by 3, approximately 0.38
Now, we can check if this value holds for the other sets of data:
4.56 equals 12 times 0.38
6.08 equals 16 times 0.38
Since the constant of proportionality (k) is consistent across all sets, we can conclude that the constant of proportionality between the total cost and the number of songs is approximately 0.38.