Question

A business owner is monitoring the production cost of making laptop computers. It costs $5,000 to start the business. The production cost for 10 computers totals $6,000, and the production cost for 20 computers totals $5,000. Which type of function would best model the data, and why?

1) quadratic, because the production cost decreases to a minimum of $5,000 and then increases
2) quadratic, because the production cost increases to a maximum of $5,000 and then decreases
3) quadratic, because the production cost decreases to a minimum of $6,000 and then increases
4) quadratic, because the production cost increases to a maximum of $6,000 and then decreases

Answer 1

The type of function that best models the data is quadratic, because the production cost decreases to a minimum of $6,000 and then increases.

Step-by-step explanation:

The type of function that best models the data is option 3) quadratic, because the production cost decreases to a minimum of $6,000 and then increases.

Quadratic functions have a parabolic shape, and they can have a minimum or a maximum point. In this case, the production cost starts at $6,000 for 10 computers, decreases to a minimum of $5,000 for 20 computers, and then increases again. This trend matches the shape of a quadratic function.

Therefore, the best model for the data is a quadratic function that has a minimum point at $6,000 for 20 computers and then increases.