a window washer drops a bucket from 650 meters above a sidewalk. the bucket’s height h(t), in meters, above…

a window washer drops a bucket from 650 meters above a sidewalk. the bucket’s height h(t), in meters, above the sidewalk is modeled by the function h(t)= -4.9t² + 650, where t is the time in seconds since the bucket was dropped. what is the average rate of change, in meters per second, in the bucket’s height above the sidewalk between 5 and 8 seconds, to the nearest tenth?

a window washer drops a bucket from 650 meters above a sidewalk. the bucket’s height h(t), in meters, above the sidewalk is modeled by the function h(t)= -4.9t² + 650, where t is the time in seconds since the bucket was dropped. what is the average rate of change, in meters per second, in the bucket’s height above the sidewalk between 5 and 8 seconds, to the nearest tenth?

Answer

Explanation:

Step1: Find $h(5)$

Substitute $t = 5$ into $h(t)=-4.9t^{2}+650$. $h(5)=-4.9\times5^{2}+650=-4.9\times25 + 650=-122.5+650 = 527.5$

Step2: Find $h(8)$

Substitute $t = 8$ into $h(t)=-4.9t^{2}+650$. $h(8)=-4.9\times8^{2}+650=-4.9\times64+650=-313.6 + 650=336.4$

Step3: Calculate average rate of change

The formula for average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 5$, $b = 8$, $f(t)=h(t)$. Average rate of change$=\frac{h(8)-h(5)}{8 - 5}=\frac{336.4 - 527.5}{3}=\frac{-191.1}{3}=-63.7$

Answer:

$-63.7$