Question

a ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. the graph below shows the height, y, of the ball from the ground after x seconds.
what is the approximate average rate of change, in height per second, when the time is 0 seconds to when the height is maximum? interpret your answer.
solution:
initial point is:
maximum point is:
average rate of change =
interpret your answer:

Explanation:

Step1: Identify key points

Initial point (time=0): $(0, 48)$; Maximum point: $(2.5, 148)$

Step2: Calculate average rate of change

Use formula $\frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$
$\text{Average rate of change} = \frac{148 - 48}{2.5 - 0} = \frac{100}{2.5} = 40$

Step3: Interpret the result

The value represents height change per second.

Answer:

Average rate of change = 40 feet per second
Interpretation: Between 0 and 2.5 seconds, the ball's height increases by an average of 40 feet each second as it travels upward to its maximum height of 148 feet.