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The table below gives the cost per person to rent a fishing charter boat. Find the rate of change given that it is constant. Also, explain what the rate of change means for this situation.

\begin{tabular}{|c|c|}
\hline People & Cost (\[tex]$) \\
\hline 2 & 110 \\
\hline 3 & 165 \\
\hline 4 & 220 \\
\hline 5 & 275 \\
\hline
\end{tabular}

A. $[/tex]\frac{1}{55}[tex]$
B. $[/tex]\frac{110}{1}[tex]$
C. $[/tex]\frac{1}{215}[tex]$
D. $[/tex]\frac{55}{1}$



Answer :

GinnyAnswer
Let's analyze the problem step-by-step to find the rate of change.

1. Determine the Costs for Different Numbers of People:
- For 2 people, the cost is \[tex]$110. - For 3 people, the cost is \$[/tex]165.

2. Find the Difference in Costs:
- The difference in cost between 3 people and 2 people is:
[tex]\[ 165 - 110 = 55 \][/tex]

3. Find the Difference in the Number of People:
- The difference in the number of people between 3 people and 2 people is:
[tex]\[ 3 - 2 = 1 \][/tex]

4. Calculate the Rate of Change:
- The rate of change is given by the difference in cost divided by the difference in the number of people:
[tex]\[ \text{Rate of Change} = \frac{\text{Difference in Cost}}{\text{Difference in Number of People}} = \frac{55}{1} = 55 \][/tex]

The rate of change is 55. This means that for every additional person, the cost increases by [tex]$55. 5. Interpretation of the Rate of Change: - The rate of change in this context means the additional cost incurred for each additional person joining the fishing charter boat. Therefore, each additional person costs \$[/tex]55 more.

In conclusion, the rate of change, given that it is constant, is:
[tex]\[ \frac{55}{1} = 55 \][/tex]

From the given options, the correct answer is:
[tex]\[ \boxed{\frac{55}{1}} \][/tex]

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