A travel agency made the table to represent the profits it makes on a certain vacation package. Number of People vs. Profit Number of People Who Buy the Package, x Profit per Person (in dollars), y 10 500 20 800 30 900 40 800 50 500 Which of the following explains the best model for the data in the table?
Answer
A
an exponential function since the ratios of the y -values are about the same
B
a quadratic function since the points lie on a curve that is symmetric about the line x is equal to 30
C
a linear function since the profit per person changes by 30 dollars for each additional person
D
an absolute value function since the values increase and then decrease
Explanation
The profits are symmetric around x = 30: the values at x = 10 and x = 50 are both 500, and the values at x = 20 and x = 40 are both 800. The maximum profit, 900, occurs at x = 30, so the data fit a curve symmetric about the vertical line x = 30. A quadratic function models this pattern, so the best choice is a quadratic function.
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