Question

the graph shows the height in feet of a bottle rocket over time in seconds. complete the statement below with a number: \the average rate of change in the height of the rocket from 0.5 seconds to 2.75 seconds is a decrease of feet per second.\ (0.5,30.5) (1.5,43.5) (2.25,32.25) (2.75,14.75)

Explanation:

Step1: Identify the height - time pairs

At $t_1 = 0.5$ seconds, $h_1=30.5$ feet; at $t_2 = 2.75$ seconds, $h_2 = 14.75$ feet.

Step2: Use the average - rate - of - change formula

The formula for the average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, the function is height $h$ in terms of time $t$, so the average rate of change of height with respect to time from $t_1$ to $t_2$ is $\frac{h_2 - h_1}{t_2 - t_1}$.
Substitute the values: $h_2 - h_1=14.75 - 30.5=-15.75$ and $t_2 - t_1=2.75 - 0.5 = 2.25$.

Step3: Calculate the average rate of change

$\frac{h_2 - h_1}{t_2 - t_1}=\frac{-15.75}{2.25}=-7$.

Answer:

7