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.
Accepted Solution
A:
Answer:Average rate of change: 0Interpretation: No increment in yield from year 5 to year 15.Step-by-step explanation:The function that models the yield is: [tex]f(x)=-x^2+20x+75[/tex][tex]f(15)=-(15)^2+20(15)+75=150[/tex][tex]f(5)=-(5)^2+20(5)+75=150[/tex]The average rate of change of f(x) from x=a to x=b is given by the formula;[tex]AOC=\frac{f(b)-f(a)}{b-a}[/tex]The average rate of change from year 5 to year 15 is:[tex]\frac{f(15)-f(5)}{15-5}[/tex][tex]\frac{150-150}{15-5}[/tex][tex]\frac{0}{10}=0[/tex]Interpretation: There has not been any increment in yield from year 5 to year 15.