Question

In farming, the relationship between precipitation during the growing season and crop yield is quadratic. The following table shows the amount of rainfall (in inches) with corresponding soybean crop yields (in bushels per acre) for an agricultural region.

Use a quadratic regression calculator to write a quadratic function that provides a reasonable fit to this set of data. According to the function model, about how many bushels per acre of soybeans would you expect if there was 5 inches of rain during the growing season?
A. 43.9 bushels per acre
B. 44.1 bushels per acre
C. 44.5 bushels per acre
D. 45.5 bushels per acre

Answer 1

To find a quadratic function that provides a reasonable fit to the data, use a quadratic regression calculator and substitute x = 5 to estimate the soybean crop yield.

Step-by-step explanation:

To find a quadratic function that provides a reasonable fit to the data, we can use a quadratic regression calculator. The quadratic function has the general form: y = ax^2 + bx + c. We can use the rainfall (in inches) as the independent variable x and the crop yields (in bushels per acre) as the dependent variable y. By inputting the data into the calculator, we can obtain the values of a, b, and c. Once we have the quadratic function, we can substitute x = 5 to estimate the soybean crop yield.

1. Input the data into a quadratic regression calculator, such as a graphing calculator or an online regression calculator.
2. Obtain the values of a, b, and c in the quadratic function y = ax^2 + bx + c.
3. Substitute x = 5 into the quadratic function and calculate the estimated soybean crop yield.