Average rate of change is 0
Interpretation: The crop yield did not change from year 5 to year 15
Solution:
The function that models the yield is:
[tex]f(x) = -x^2 + 20x + 75[/tex]
The average rate of change of f(x) from x = a to x = b is given by the formula:
[tex]\text{ average rate of change }=\frac{f(b)-f(a)}{b-a}[/tex]
Find and interpret the average rate of change from year 5 to year 15
[tex]f(5) = -(5)^2 + 20(5) + 75\\\\f(5) = -25 + 100 + 75\\\\f(5) = 150[/tex]
[tex]f(15) = - (15)^2 + 20(15) + 75\\\\f(15) = -225 + 300 + 75\\\\f(15) = 150[/tex]
Thus average rate of change:
[tex]\text {average rate of change}=\frac{f(15)-f(5)}{15-5}[/tex]
[tex]\text {average rate of change}=\frac{150-150}{10}=0[/tex]
Thus Average rate of change is 0
Interpretation: The crop yield did not change from year 5 to year 15.
Answer:
The option that is correct in this question is D.
Step-by-step explanation:
