Question

the average rate of change from x = 0 to x = 15 is about - 4.667. how does the average rate of change from x = 0 to x = 20 compare to this number? the average rate of change from x = 0 to x = 20 is decreasing the average rate of change from x = 0 to x = 15.

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) from \(x = a\) to \(x = b\) is \(\frac{f(b)-f(a)}{b - a}\).

Step2: Find the values for \(x = 0\) and \(x = 15\)

Assume the horizontal distance is \(x\) (independent variable) and height is \(y\) (dependent variable). Let \(x_1=0,y_1 = 20\) and \(x_2 = 15,y_2=30\).
Using the formula \(\frac{y_2 - y_1}{x_2 - x_1}=\frac{30 - 20}{15-0}=\frac{10}{15}=\frac{2}{3}\approx - 0.667\) (negative because the height is decreasing as \(x\) increases).

Answer:

The average rate of change from \(x = 0\) to \(x = 15\) is about \(-0.667\). Since \(- 0.667> - 4.667\), the average rate of change from \(x = 0\) to \(x = 15\) is greater (less negative) than the average rate of change from \(x = 0\) to \(x = 20\).