during the first 10 years of growth the height of a tree can be modeled with the function $h = -0.5t^{2}+11t…
during the first 10 years of growth the height of a tree can be modeled with the function $h = -0.5t^{2}+11t + 8$, where $t$ is the time in years since being planted and $h$ is the height in inches. what was the average rate of change, in inches per year, from year 2 to year 10? the average rate of change was inches per year.
Answer
Explanation:
Step1: Find height at year 2
Substitute $t = 2$ into $h=-0.5t^{2}+11t + 8$. $h_1=-0.5\times(2)^{2}+11\times2 + 8=-0.5\times4+22 + 8=-2+22 + 8=28$
Step2: Find height at year 10
Substitute $t = 10$ into $h=-0.5t^{2}+11t + 8$. $h_2=-0.5\times(10)^{2}+11\times10 + 8=-0.5\times100+110 + 8=-50+110 + 8=68$
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, $a = 2$, $b = 10$, $h_1$ and $h_2$ are the function - values. Average rate of change$=\frac{h_2 - h_1}{10 - 2}=\frac{68 - 28}{8}=\frac{40}{8}=5$
Answer:
5