Question

A farmer is tracking the number of soybeans his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 100 models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 10 to year 20.

Answer 1

The farmer should expect to LOSE 10 pounds of soybeans per acre per year

Explanation:

f(x)=-x^2 + 20x + 100

just find how many soybeans his land will yield (per acre) after 10 and 20 years:

After 10: 200 pounds of soybeans/acre

After 20: 100 pounds of soybeans/acre

Because 10 years have passed and they lost 100 pounds of soybean production per acre, the farmer should expect to lose 10 pounds of soybeans per acre per year (-10 pounds of soybeans per acre/year)