leila is driving a racecar. the table below gives the distance d(t) (in meters) she has driven at a few…

leila is driving a racecar. the table below gives the distance d(t) (in meters) she has driven at a few times t (in seconds) after she starts. (a) find the average rate of change for the distance driven from 0 seconds to 2 seconds. meters per second (b) find the average rate of change for the distance driven from 4 seconds to 10 seconds. meters per second

leila is driving a racecar. the table below gives the distance d(t) (in meters) she has driven at a few times t (in seconds) after she starts. (a) find the average rate of change for the distance driven from 0 seconds to 2 seconds. meters per second (b) find the average rate of change for the distance driven from 4 seconds to 10 seconds. meters per second

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = D(t)$ over the interval $[t_1,t_2]$ is $\frac{D(t_2)-D(t_1)}{t_2 - t_1}$.

Step2: Solve part (a)

For the interval from $t_1 = 0$ to $t_2=2$, $D(0) = 0$ and $D(2)=71.2$. Then the average rate of change is $\frac{D(2)-D(0)}{2 - 0}=\frac{71.2-0}{2}=35.6$.

Step3: Solve part (b)

For the interval from $t_1 = 4$ to $t_2 = 10$, $D(4)=166.4$ and $D(10)=239.6$. Then the average rate of change is $\frac{D(10)-D(4)}{10 - 4}=\frac{239.6 - 166.4}{6}=\frac{73.2}{6}=12.2$.

Answer:

(a) 35.6 (b) 12.2