MATH SOLVE

3 months ago

Q:
# A farmer is tracking the amount of corn his land is yielding each year. He finds that the function f(x) = βx2 + 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.

Accepted Solution

A:

Answer:The crop yield decreased by 0.09 pounds per acre from year 1 to year 10Step-by-step explanation:The function that models the crops in pounds per acre over x years is [tex]f(x)=-x^2+20x+50[/tex]In year 1, the crop yield is [tex]f(1)=-(1)^2+20(1)+50=69[/tex]In year 10, the crop yield is [tex]f(10)=-(10)^2+20(10)+50=150[/tex]The average rate of change from year 1 to year 10 is given by:[tex]\frac{f(10)-f(1)}{10-1}[/tex]We substitute the values to get:[tex]\frac{150-69}{10-1}[/tex][tex]=\frac{81}{9}=9[/tex]Since the average rate of change is positive, the crop yield decreased by 0.09 pounds per acre from year 1 to year 10.