question 2 (multiple choice worth 1 points) (08.01 mc) a farmer is tracking the amount of wheat his land is…

question 2 (multiple choice worth 1 points) (08.01 mc) 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. 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 2 (multiple choice worth 1 points) (08.01 mc) 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. 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.

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 5$, $b = 15$, and $f(x)=-x^{2}+20x + 75$.

Step2: Calculate $f(5)$

Substitute $x = 5$ into $f(x)$: $f(5)=-(5)^{2}+20\times5 + 75=-25 + 100+75=150$.

Step3: Calculate $f(15)$

Substitute $x = 15$ into $f(x)$: $f(15)=-(15)^{2}+20\times15 + 75=-225+300 + 75=150$.

Step4: Calculate the average rate of change

$\frac{f(15)-f(5)}{15 - 5}=\frac{150 - 150}{10}=0$.

Answer:

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