during the first years of growth, the height of a tree can be modeled with the function, h = -t² + 12t + 10…
during the first years of growth, the height of a tree can be modeled with the function, h = -t² + 12t + 10, where t is the time in years since being planted and h is the height in inches. enter the average rate of change, in inches per year, from year 1 to year 5. the average rate of change of the trees height from year 1 to year 5 is inches per year. 12.78 6 46 -0.78
Answer
Explanation:
Step1: Find height at t = 1
Substitute t = 1 into $h=-t^{2}+12t + 10$. $h_1=-(1)^{2}+12\times1 + 10=-1 + 12+10=21$.
Step2: Find height at t = 5
Substitute t = 5 into $h=-t^{2}+12t + 10$. $h_2=-(5)^{2}+12\times5 + 10=-25+60 + 10=45$.
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, $a = 1$, $b = 5$, $h_1$ is $f(1)$ and $h_2$ is $f(5)$. $\frac{h_2 - h_1}{5 - 1}=\frac{45-21}{4}=\frac{24}{4}=6$.
Answer:
6