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]
