A farmer is tracking the amount of wheat his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 75 models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 5 to year 15. (1 point)

The crop yield increased by 150 pounds per acre from year 5 to year 15.

The crop yield decreased by 15 pounds per acre from year 5 to year 15.

The crop yield decreased by 5 pounds per acre from year 5 to year 15.

The crop yield did not change from year 5 to year 15.

Question

A farmer is tracking the amount of wheat his land is yielding each year. He finds that the function f(x) = −x2 + 20x + 75 models the crops in pounds per acre over x years. Find and interpret the average rate of change from year 5 to year 15. (1 point)

The crop yield increased by 150 pounds per acre from year 5 to year 15.

The crop yield decreased by 15 pounds per acre from year 5 to year 15.

The crop yield decreased by 5 pounds per acre from year 5 to year 15.

The crop yield did not change from year 5 to year 15.

Luigi0210 · Answer

Since x represents the time, you can plug those into the equation to give you the y value, aka the pounds/acre

$$\large f(5)= -(5)^2 +20(5) +75 = -25+100+75=150 $$
$$\large f(15) = -(15)^5 +20(15)+75 = -225 +300+75 = 150$$

As you can see, there is no change from year 5 to year 15.