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.

Answer 1

Average rate of change: 0

Interpretation: No increment in yield from year 5 to year 15.

Explanation:

The function that models the yield is:

`f(x)=-x^2+20x+75`

`f(15)=-(15)^2+20(15)+75=150`

`f(5)=-(5)^2+20(5)+75=150`

The average rate of change of f(x) from x=a to x=b is given by the formula;

`AOC=(f(b)-f(a))/(b-a)`

The average rate of change from year 5 to year 15 is:

`(f(15)-f(5))/(15-5)`

`(150-150)/(15-5)`

`(0)/(10)=0`

Interpretation: There has not been any increment in yield from year 5 to year 15.