ann launches a rocket straight up into the air. the table below gives the height h(t) of the rocket (in…

ann launches a rocket straight up into the air. the table below gives the height h(t) of the rocket (in meters) at a few times t (in seconds) during its flight. time t (seconds) height h(t) (meters) 0 0 2.2 110 6.6 198 8.8 44 13.2 0 (a) find the average rate of change for the height from 0 seconds to 2.2 seconds. meters per second (b) find the average rate of change for the height from 6.6 seconds to 8.8 seconds. meters per second

ann launches a rocket straight up into the air. the table below gives the height h(t) of the rocket (in meters) at a few times t (in seconds) during its flight. time t (seconds) height h(t) (meters) 0 0 2.2 110 6.6 198 8.8 44 13.2 0 (a) find the average rate of change for the height from 0 seconds to 2.2 seconds. meters per second (b) find the average rate of change for the height from 6.6 seconds to 8.8 seconds. meters per second

Answer

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 height function $H(t)$, the average rate of change from $t=a$ to $t = b$ is $\frac{H(b)-H(a)}{b - a}$.

Step2: Solve part (a)

We have $a = 0$, $b=2.2$, $H(0)=0$, and $H(2.2)=110$. Using the formula $\frac{H(2.2)-H(0)}{2.2 - 0}=\frac{110 - 0}{2.2}=\frac{110}{2.2}=50$.

Step3: Solve part (b)

We have $a = 6.6$, $b = 8.8$, $H(6.6)=198$, and $H(8.8)=44$. Using the formula $\frac{H(8.8)-H(6.6)}{8.8 - 6.6}=\frac{44-198}{8.8 - 6.6}=\frac{- 154}{2.2}=-70$.

Answer:

(a) 50 (b) - 70