a function is graphed below. on which interval of x is the average rate of change of the function the…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Calculate average rate of change for $x = 1$ to $x = 5$

Let $a = 1$, $b = 5$, $f(1)=100$, $f(5)=400$. Then $\frac{f(5)-f(1)}{5 - 1}=\frac{400 - 100}{4}=\frac{300}{4}=75$.

Step3: Calculate average rate of change for $x = 5$ to $x = 16$

Let $a = 5$, $b = 16$, $f(5)=400$, $f(16)=800$. Then $\frac{f(16)-f(5)}{16 - 5}=\frac{800 - 400}{11}=\frac{400}{11}\approx36.36$.

Step4: Calculate average rate of change for $x = 10$ to $x = 29$

Let $a = 10$, $b = 29$, $f(10)=600$, $f(29)=1000$. Then $\frac{f(29)-f(10)}{29 - 10}=\frac{1000 - 600}{19}=\frac{400}{19}\approx21.05$.

Step5: Calculate average rate of change for $x = 29$ to $x = 47$

Let $a = 29$, $b = 47$, $f(29)=1000$, $f(47)=1200$. Then $\frac{f(47)-f(29)}{47 - 29}=\frac{1200 - 1000}{18}=\frac{200}{18}=\frac{100}{9}\approx11.11$.

Answer:

$x = 29$ to $x = 47$