given the function defined in the table below, find the average rate of change, in simplest form, of the…

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 25 ≤ x ≤ 85.\n| x | f(x) |\n|----|----|\n| 10 | 52 |\n| 25 | 43 |\n| 40 | 34 |\n| 55 | 25 |\n| 70 | 16 |\n| 85 | 7 |

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 25 ≤ x ≤ 85.\n| x | f(x) |\n|----|----|\n| 10 | 52 |\n| 25 | 43 |\n| 40 | 34 |\n| 55 | 25 |\n| 70 | 16 |\n| 85 | 7 |

Answer

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 $\frac{f(b)-f(a)}{b - a}$. Here, $a = 25$, $b = 85$, $f(25)=43$, and $f(85)=7$.

Step2: Substitute values into formula

$\frac{f(85)-f(25)}{85 - 25}=\frac{7 - 43}{85 - 25}$.

Step3: Simplify the numerator and denominator

The numerator $7-43=-36$, and the denominator $85 - 25 = 60$. So we have $\frac{-36}{60}$.

Step4: Reduce the fraction

Dividing both the numerator and denominator by their greatest - common divisor (which is 12), we get $\frac{-36\div12}{60\div12}=-\frac{3}{5}$.

Answer:

$-\frac{3}{5}$