the height of a leaf, h, being carried by the wind is a function of time, t, since the observation began…

the height of a leaf, h, being carried by the wind is a function of time, t, since the observation began. the graph of the function is shown below. the following points are visible on the graph: (4,16) and (7,6). which expression correctly calculates the average rate of change of the function for the interval of time from 4 seconds to 7 seconds? time (seconds)

the height of a leaf, h, being carried by the wind is a function of time, t, since the observation began. the graph of the function is shown below. the following points are visible on the graph: (4,16) and (7,6). which expression correctly calculates the average rate of change of the function for the interval of time from 4 seconds to 7 seconds? time (seconds)

Answer

Answer:

The formula for the average rate of change of a function $y = f(x)$ over the interval $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Here, $x_1 = 4$, $f(x_1)=16$, $x_2 = 7$, and $f(x_2)=6$. So the average rate of change is $\frac{6 - 16}{7-4}$.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y=f(x)$ over $[x_1,x_2]$ is $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$.

Step2: Identify values of $x_1$, $x_2$, $f(x_1)$ and $f(x_2)$

Given $x_1 = 4$, $f(x_1)=16$, $x_2 = 7$, $f(x_2)=6$.

Step3: Substitute values into formula

Substitute into $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$ to get $\frac{6 - 16}{7-4}$.