Too Many Corn Plants per Acre? The more corn a farmer plants per acre, the greater the yield the farmer can expect, but only up to a point. Too many plants per acre can cause overcrowding and decrease yields. The data give crop yields per acre for various densities of corn plantings, as found by researchers at a university test farm.

(a) Find the quadratic polynomial that best fits the data.

(b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data.

(c) Use your result from part (b) to estimate the yield for 37,000 plants per acre.

Density Crop yield

(plants/acre) (bushels/acre)

15,000 43

20,000 98

25,000 118

30,000 140

35,000 142

40,000 122

45,000 93

50,000 67