a travel agency made the table below to represent the profits it makes on a certain vacation package. number…

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

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

Explanation:

Step1: Analyze the data trend

The profit - per - person ($y$) values first increase from 500 to 900 as the number of people ($x$) increases from 10 to 30, and then decrease from 900 to 500 as $x$ increases from 30 to 50.

Step2: Evaluate each option

  • Absolute - value function: An absolute - value function can have a graph that increases and then decreases. This is consistent with the data trend.
  • Exponential function: The ratios of the $y$ - values are not about the same. For example, $\frac{800}{500}=1.6$, $\frac{900}{800} = 1.125$, so it's not an exponential function.
  • Linear function: The profit per person does not change by a constant amount ($30$ is incorrect). For $x$ from 10 to 20, $y$ changes from 500 to 800 (a change of 300), for $x$ from 20 to 30, $y$ changes from 800 to 900 (a change of 100).
  • Quadratic function: There is no indication that the points lie on a curve symmetric about $x = 30$. Just because the values increase and then decrease does not mean it's a quadratic symmetric about $x=30$.

Answer:

an absolute value function since the values increase and then decrease