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Sagot :
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: \[ \$[/tex] 4.80 \text{ per ticket}
\]
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: \[ \$[/tex] 4.80 \text{ per ticket}
\]
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