The table shows the cost of a ski rental package for a given number of people. Using the rate of change, what is the cost for 13 people?

People Cost ($)
2 70
3 105
4 140
5 175

There are 4 answer choices - 560, 440, 520, 480. I got 455. Am I wrong?

No you're right!(;

To find the rate of change, we can calculate the slope of the line passing through the given points (2, 70), (3, 105), (4, 140), and (5, 175).

Let's calculate the slope between the first two points:
Slope = (105 - 70) / (3 - 2) = 35 / 1 = 35

Now, let's calculate the slope between the next two points:
Slope = (140 - 105) / (4 - 3) = 35 / 1 = 35

And finally, let's calculate the slope between the last two points:
Slope = (175 - 140) / (5 - 4) = 35 / 1 = 35

Since the slope remains constant at 35, this indicates that the cost increases by $35 for each additional person.

Therefore, to find the cost for 13 people, we can use the formula:

Cost = cost for 5 people + (number of additional people) * (rate of change)
Cost = 175 + (13 - 5) * 35
Cost = 175 + 8 * 35
Cost = 175 + 280
Cost = 455

Your answer of 455 is indeed correct. None of the provided answer choices matches the correct cost for 13 people.

To find the cost for 13 people using the rate of change, we should first observe the pattern in the table.

We can see that as the number of people increases by 1, the cost increases by $35. This means that the rate of change between the number of people and the cost is constant and equal to $35.

Now let's calculate the cost for 13 people by applying the rate of change.

Starting from 2 people, we need to add $35 to the cost for each additional person:

2 people: $70
3 people: $70 + $35 = $105
4 people: $105 + $35 = $140
...
13 people: $70 + ($35 multiplied by 11) = $70 + $385 = $455

Therefore, based on the rate of change observed in the table, the cost for 13 people should be $455.

Among the given answer choices, none matches $455. However, it's important to note that the answer choices provided may not be exhaustive, and there might be other possible answers beyond the provided choices.