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Using the table below, what is the rate of change? Don't forget to include your units.

\begin{tabular}{|c|c|c|c|c|}
\hline Number of tickets & 25 & 30 & 35 & 40 \\
\hline Total Cost (\[tex]$) & 120 & 144 & 168 & 192 \\
\hline
\end{tabular}

A. \$[/tex]24 per ticket
B. \[tex]$4.17 per ticket
C. \$[/tex]4.80 per ticket
D. \$0.21 per ticket


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