3. a football is kicked in the air. the heigh...
3. a football is kicked in the air. the height, h(t), in feet of the football is a function of time, t, in seconds, as shown in the table below.\n| t | 0 |.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 |\n| h(t) | 0 | 36 | 64 | 84 | 96 | 100 | 96 | 84 | 64 | 36 | 0 |\nwrite a statement that would represent the average rate of change of this function from t = 1.5 to t = 3?
Answer
# Explanation:
## Step1: Recall average rate - of - change formula
The average rate of change of a function $y = h(t)$ from $t = a$ to $t = b$ is given by $\frac{h(b)-h(a)}{b - a}$. Here, $a = 1.5$, $b = 3$, $h(1.5)=84$, and $h(3)=96$.
## Step2: Substitute values into formula
$\frac{h(3)-h(1.5)}{3 - 1.5}=\frac{96 - 84}{3 - 1.5}$.
## Step3: Calculate the result
$\frac{96 - 84}{3 - 1.5}=\frac{12}{1.5}=8$.
The statement is: The average rate of change of the height function of the football from $t = 1.5$ seconds to $t = 3$ seconds is 8 feet per second.
# Answer:
The average rate of change of the height function of the football from $t = 1.5$ seconds to $t = 3$ seconds is 8 feet per second.