given the function defined in the table below, find the average r of the function over the interval 30 ≤ x ≤…

given the function defined in the table below, find the average r of the function over the interval 30 ≤ x ≤ 60.\n x f(x)\n 0 7\n 15 10\n 30 13\n 45 16\n 60 19\n 75 22

given the function defined in the table below, find the average r of the function over the interval 30 ≤ x ≤ 60.\n x f(x)\n 0 7\n 15 10\n 30 13\n 45 16\n 60 19\n 75 22

Answer

Explanation:

Step1: Recall average - rate formula

The average rate of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 30$, $b = 60$, $f(a)=f(30)=13$, and $f(b)=f(60)=19$.

Step2: Calculate the average rate

Substitute the values into the formula: $\frac{f(60)-f(30)}{60 - 30}=\frac{19 - 13}{30}$. Simplify the numerator: $19-13 = 6$. So, $\frac{6}{30}=\frac{1}{5}=0.2$.

Answer:

$0.2$