Question

If x represents the time the average rate of change of function in the first two seconds is

Answer 1

average rate of change = slope

Use slope formula. (Rise over Run)


`m = (y_2 - y_1)/(x_2 - x_1)`

look at the 2 points where x=0 and x = 2, this interval covers the first 2 seconds.

f(0) = 50, f(2) = 100


`m = (100 -50)/(2-0) = (50)/(2) = 25`

The avg rate of change is 25 units per second.

Answer 2

Rate of change of function in first 2 seconds is
`25` units per second.

Explanation:

Average rate of change of a function is its gradient/slope (m)

Gradient or the rate of change can be calculated by the following equation,

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

Here
`y_(1)` refers to a certain y axis value of the line drawn and
`x_(1)` is the x value that corresponds to that y value.
`y_(2)` and
`x_(2)` operates with same logic.

Lets pick a y value from the graph,

`y_(1)` = 100

So the x value corresponding to that (
`x_(1)`) would be 2

Lets pick another y value from the graph.

[tex]y_{2}[/tex] = 50

So the x value corresponding to that (
`x_(2)`) would be 0

So by substituting to the equation for gradient or the rate of change,

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

=
`m=(100-50)/(2-0)`

=
`m=(50)/(2)`

=
`25`

The graph is a linear graph so the rate of change of function is the same in every position.

Therefore the Rate of change of function in first 2 seconds is
`25` units per second.