Question

1. a stone is thrown up from the edge of a cliff and then falls into the sea below. its height, in feet, is modeled as a function of time, in seconds. consider this graph of the function. estimate, to the nearest whole number, the average rate of change (slope) of the height of the stone for the first 2 seconds.

the estimated average rate of change for the first 2 seconds is
ft/sec.

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 0\), \(b=2\).

Step2: Estimate the function values from the graph

From the graph, when \(x = 0\) (time \(t = 0\) seconds), the height \(y=f(0)\approx10\) feet. When \(x = 2\) (time \(t = 2\) seconds), the height \(y = f(2)\approx2\) feet.

Step3: Calculate the average rate of change

Substitute into the formula \(\frac{f(2)-f(0)}{2-0}=\frac{2 - 10}{2}=\frac{-8}{2}=- 4\)

Answer:

\(-4\)