Question

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Answer 1

Answer:

the answer is The crop yield did not change from year 5 to year 15

Step-by-step explanation:

Answer 2

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:

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

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

$\text{ average rate of change }=\frac{f(b)-f(a)}{b-a}$

Find and interpret the average rate of change from year 5 to year 15

$f(5) = -(5)^2 + 20(5) + 75\\\\f(5) = -25 + 100 + 75\\\\f(5) = 150$

$f(15) = - (15)^2 + 20(15) + 75\\\\f(15) = -225 + 300 + 75\\\\f(15) = 150$

Thus average rate of change:

$\text {average rate of change}=\frac{f(15)-f(5)}{15-5}$

$\text {average rate of change}=\frac{150-150}{10}=0$

Thus Average rate of change is 0

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