Question

The table below shows the profit based on price for an object sold by a company.

A 2-column table with 6 rows. The first column is labeled price per unit (dollar sign) with entries 0, 10, 20, 30 ,40, 50. The second column is labeled profit (dollar sign) with entries negative 4,000; 12,500; 24,000; 32,500; 36,000; 35,500.
Which statements are true? Check all that apply.

The data is best represented by an exponential model.
The data is best represented by a quadratic model.
If the price is $5 per unit, the expected profit is approximately $4,686.
If the price is $80 per unit, the expected profit is negative.
As the price per unit increases, the profit increases indefinitely.

Answer 1

Select:
- The data is best represented by a quadratic model. (True)
- If the price is $5 per unit, the expected profit is approximately $4,686. (True)

Reasoning (brief):
- The profits rise then fall slightly (peak near 40–50), so the pattern is parabolic (quadratic), not exponential.
- A least-squares quadratic fit is approximately y = −20.8929 x^2 + 1834.6429 x − 3964.2857, which gives y(5) ≈ 4686.6.
- Using that quadratic, y(80) ≈ 9093 (positive), so “profit is negative at $80” is false.
- Because the quadratic opens downward (negative leading coefficient), profit does not increase indefinitely (that statement is false).