Question

If x represents time, the average rate of change of the function f(x) in the first three seconds is ___.

Answer 1

If x represents time, the average rate of change of the function f(x) in the first three seconds is -50.

Step-by-step explanation

The average rate of change of a linear function is the slope of the liner function. To find the slope of our linear function, we are using the slope formula:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

where

`m` is the slope of the line

`(x_(1),y_(1))` are the coordinates of the first point on the line

`(x_(2),y_(2))` are the coordinates of the second point

From our graph we can get the points (0, 150) and (3, 0), so
`x_(1)=0`,
`y_(1)=150`,
`x_(2)=3`, and
`y_(2)=0`. Let's replace the values in our formula to find the slope of our linear function:

`m=(0-150)/(3-0)`

`m=(-150)/(3)`

`m=-50`

Since the average of change a linear function is equal to its slope, the average rate of change of the function in the first three seconds is -50