To determine the rate of change using the given data, we need to understand the change in the total cost with respect to the change in the number of tickets. Here's a step-by-step solution:
1. Identify the changes in the number of tickets and the total cost between any two consecutive points.
- Let's start with the first two data points:
- Number of tickets: 25 to 30
- Total cost: \[tex]$120 to \$[/tex]144
2. Calculate the change in the number of tickets (Δtickets):
[tex]\[
\Delta \text{tickets} = 30 - 25 = 5
\][/tex]
3. Calculate the change in the total cost (Δcosts):
[tex]\[
\Delta \text{costs} = 144 - 120 = 24\: \$
\][/tex]
4. Determine the rate of change:
The rate of change is the ratio of the change in the total cost to the change in the number of tickets.
[tex]\[
\text{Rate of change} = \frac{\Delta \text{costs}}{\Delta \text{tickets}} = \frac{24}{5} = 4.80\: \text{\$/ticket}
\][/tex]
5. Conclusion:
The rate of change in the cost per ticket is \[tex]$4.80 per ticket.
Therefore, the correct answer is:
\[
\$[/tex] 4.80 \text{ per ticket}
\]
