Question

Analyzing a Data Set
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

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

False:
- The data is best represented by an exponential model. (An exponential model would be monotonic; the data rises then falls, suggesting a parabola.)
- If the price is $80 per unit, the expected profit is negative. (A quadratic fit gives a positive profit at $80.)
- As the price per unit increases, the profit increases indefinitely. (The fitted quadratic opens downward and has a maximum, so profit does not increase forever.)

Supporting numbers (quadratic least-squares fit):
P(x) ≈ −20.8929 x^2 + 1834.6429 x − 3964.2857,
so P(5) ≈ $4,686.61 and P(80) ≈ $9,099.7.