Too Many Corn Plants per Acre? The more corn a farmer plants per acre, the greater is 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.
Density (plants/acre): 15,000, 20,000, 25,000, 30,000, 35,000, 40,000, 45,000, 50,000
Crop yield (bushels/acre): 43, 98, 118, 140, 142, 122, 93, 67
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.