tommy throws a ball from the balcony of his apartment down to the street. the height of the ball, in meters…

tommy throws a ball from the balcony of his apartment down to the street. the height of the ball, in meters, is modeled by the function shown in the graph. whats the average rate of change of the height of the ball, in meters per second, while its in the air?\na) -3/2\nb) 2/3\nc) -2/3\nd) 3/2

tommy throws a ball from the balcony of his apartment down to the street. the height of the ball, in meters, is modeled by the function shown in the graph. whats the average rate of change of the height of the ball, in meters per second, while its in the air?\na) -3/2\nb) 2/3\nc) -2/3\nd) 3/2

Answer

Explanation:

Step1: Identify start - end points

The ball starts at $t = 0$ with height $h(0)=18$ and hits the ground at $t = 12$ with height $h(12)=0$.

Step2: Use average rate of change formula

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, $a = 0$, $b = 12$, $f(a)=18$, $f(b)=0$. So the average rate of change is $\frac{0 - 18}{12-0}$.

Step3: Simplify the expression

$\frac{0 - 18}{12-0}=\frac{- 18}{12}=-\frac{3}{2}$.

Answer:

A. $-\frac{3}{2}$