tammy is driving a racecar. the table below gives the distance d(t) (in met\n\n| time t (seconds) | distance…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. For the distance function $D(t)$, the average rate of change from $t=a$ to $t = b$ is $\frac{D(b)-D(a)}{b - a}$.

Step2: Calculate average rate of change for part (a)

Here, $a = 0$, $b = 2$, $D(0)=0$, and $D(2)=71.2$. Substitute into the formula: $\frac{D(2)-D(0)}{2 - 0}=\frac{71.2-0}{2}=\frac{71.2}{2}=35.6$.

Step3: Calculate average rate of change for part (b)

Here, $a = 6$, $b = 10$, $D(6)=172.8$, and $D(10)=239.6$. Substitute into the formula: $\frac{D(10)-D(6)}{10 - 6}=\frac{239.6 - 172.8}{4}=\frac{66.8}{4}=16.7$.

Answer:

(a) 35.6 (b) 16.7