rate of change\n14. during the first years of growth the height of a tree can be modeled with the function…
rate of change\n14. during the first years of growth the height of a tree can be modeled with the function $h(t)=-t^{2}+12t + 10$ where $t$ is the time in years since being planted, and $h$ is the height in inches.\nwhat is the average rate of change, in inches per year, from year 1 to year 5?
Answer
Explanation:
Step1: Encontrar el valor de la función en $t = 1$
Sustituir $t = 1$ en $h(t)=-t^{2}+12t + 10$. $h(1)=-(1)^{2}+12(1)+10=-1 + 12+10=21$.
Step2: Encontrar el valor de la función en $t = 5$
Sustituir $t = 5$ en $h(t)=-t^{2}+12t + 10$. $h(5)=-(5)^{2}+12(5)+10=-25 + 60+10=45$.
Step3: Calcular la tasa de cambio promedio
La fórmula para la tasa de cambio promedio de una función $y = h(t)$ de $t=a$ a $t = b$ es $\frac{h(b)-h(a)}{b - a}$. Aquí, $a = 1$, $b = 5$, $h(1)=21$ y $h(5)=45$. $\frac{h(5)-h(1)}{5 - 1}=\frac{45-21}{4}=\frac{24}{4}=6$.
Answer:
6