Question 10 • TN-Algebra II B SC 26-27 (For Credit)
A travel agency made the table below to represent the profits it makes on a certain vacation package.Number of People vs. ProfitNumber of People Who Buy the Package, xProfit per Person (in dollars), y1050020800309004080050500Which of the following explains the best model for the data in the table?
Answer
A
an absolute value function since the values increase and then decrease
B
an exponential function since the ratios of the y-values are about the same
C
a linear function since the profit per person changes by $30 for each additional person
D
a quadratic function since the points lie on a curve that is symmetric about the line x = 30
Explanation
The profits rise from $500 to $900 as the number of people increases from 10 to 30, then fall back to $500 by 50 people. The values are symmetric around x = 30: the profits at 10 and 50 are equal, as are those at 20 and 40. This pattern is best modeled by a quadratic function, so the correct choice is D.
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