Question

the height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function h(t)=300 - 16t². which expression could be used to determine the average rate at which the object falls during the first 3 seconds of its fall?
\\(\frac{h(3)-h(0)}{3}\\) \\(\frac{h(3)}{3}\\) h(3)-h(0) \\(h(\frac{3}{2})-h(\frac{0}{2})\\)

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is given by $\frac{f(b)-f(a)}{b - a}$.

Step2: Identify the interval and function

The function for the height of the falling object is $h(t)=300 - 16t^{2}$, and the interval is $[0,3]$ (since we want to find the average rate of fall in the first 3 seconds, starting from $t = 0$).

Step3: Apply the formula

Using the average - rate - of - change formula with $a = 0$, $b = 3$, and $y=h(t)$, we get $\frac{h(3)-h(0)}{3 - 0}=\frac{h(3)-h(0)}{3}$.

Answer:

$\frac{h(3)-h(0)}{3}$ (the first option)