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

a travel agency made the table below to represent the profits it makes on a certain vacation package.\nnumber of people vs. profit\nnumber of people who buy the package, x\tprofit per person (in dollars), y\n10\t500\n20\t800\n30\t900\n40\t800\n50\t500\nwhich of the following explains the best model for the data in the table?\nan absolute - value function since the values increase and then decrease\nan exponential function since the ratios of the y - values are about the same\na linear function since the profit per person changes by $30 for each additional person\na 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.\nnumber of people vs. profit\nnumber of people who buy the package, x\tprofit per person (in dollars), y\n10\t500\n20\t800\n30\t900\n40\t800\n50\t500\nwhich of the following explains the best model for the data in the table?\nan absolute - value function since the values increase and then decrease\nan exponential function since the ratios of the y - values are about the same\na linear function since the profit per person changes by $30 for each additional person\na quadratic function since the points lie on a curve that is symmetric about the line x = 30

Answer

Explanation:

Step1: Analyze absolute - value function

The profit per person first increases from 500 to 900 and then decreases back to 500 as the number of people increases from 10 to 50. This pattern of increase and then decrease is characteristic of an absolute - value function.

Step2: Analyze 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.

Step3: Analyze linear function

The profit per person does not change by a constant amount ($30$ is incorrect). For example, from $x = 10$ to $x = 20$, the change in profit per person is $800 - 500=300$, not 30. So it's not a linear function.

Step4: Analyze quadratic function

There is no clear indication that the points lie on a curve symmetric about $x = 30$. The data doesn't show a parabolic - like symmetry about $x = 30$.

Answer:

an absolute value function since the values increase and then decrease