Question

A travel agency made the table below 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?
an absolute value function since the values increase and then decrease
an exponential function since the ratios of the y-values are about the same
a linear function since the profit per person changes by $30 for each additional person
a quadratic function since the points lie on a curve that is symmetric about the line x = 30

Answer 1

A quadratic function. The data are symmetric about x = 30 and fit y = 900 − (x − 30)^2 (gives 500, 800, 900, 800, 500). It is not linear (changes are not constant), not exponential (ratios vary), and not an absolute-value (changes per equal x-steps are not constant as they would be for a V-shape).