To determine the rate of change for the cost of downloading songs given in your table, let's analyze the information step-by-step:
The table shows:
- When 2 songs are downloaded, the total cost is $4.
- When 3 songs are downloaded, the total cost is $6.
- When 4 songs are downloaded, the total cost is $8.
- When 5 songs are downloaded, the total cost is $10.
First, let's understand what the rate of change represents. The rate of change is essentially how much the cost (\( y \)) increases with each additional song (\( x \)). Mathematically, this is the change in \( y \) divided by the change in \( x \).
From the table, we can see how the costs change with the number of songs. To calculate it, we can use the values in the table:
Let's take the two endpoints:
- When \( x_1 = 2 \) and \( y_1 = 4 \)
- When \( x_2 = 5 \) and \( y_2 = 10 \)
The formula for the rate of change (slope) is:
[tex]\[
\text{Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging the values from the table into the formula:
[tex]\[
\text{Rate of Change} = \frac{10 - 4}{5 - 2} = \frac{6}{3} = 2.0
\][/tex]
Therefore, the rate of change for the function in the table is \( 2.0 \). This means that the cost increases by \( \$2 \) for every additional song downloaded.
Thus, the correct interpretation of the rate of change from the given options is:
[tex]\[
\$2 \text{ per song}
\][/tex]
