A farmer is tracking the amount of corn his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 50 models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 1 to year 10.

The crop yield increased by 9 pounds per acre from year 1 to year 10.
The crop yield decreased by 0.09 pounds per acre from year 1 to year 10.
The crop yield decreased by 11 pounds per acre from year 1 to year 10.
The crop yield increased by 99 pounds per acre from year 1 to year 10.

The crop yield increased by 9 pounds per acre from year 1 to year 10.

Step-by-step explanation:

To solve this we are using the average rate of change formula: , where:

is the second point in the function

is the first point in the function

is the function evaluated at the second point

is the function evaluated at the first point

We know that the first point is 1 year and the second point is 10 years, so and . Replacing values:

Since represents the number of pounds per acre and the number of years, we can conclude that the crop yield increased by 9 pounds per acre from year 1 to year 10.

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