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

average rate of change = slope

Use slope formula. (Rise over Run)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

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

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

[tex]m = \frac{100 -50}{2-0} = \frac{50}{2} = 25[/tex]

The avg rate of change is 25 units per second.

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Limosa Limosa · Answer 2 · 2018-10-11T10:32:46+02:00

Answer:

Rate of change of function in first 2 seconds is [tex]25[/tex] units per second.

Step-by-step 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,

[tex]m=\frac{y_{1} -y_{2}}{x_{1}-x_{2}}[/tex]

Here [tex]y_{1}[/tex] refers to a certain y axis value of the line drawn and [tex]x_{1}[/tex] is the x value that corresponds to that y value. [tex]y_{2}[/tex] and [tex]x_{2}[/tex] operates with same logic.

Lets pick a y value from the graph,

[tex]y_{1}[/tex] = 100

So the x value corresponding to that ([tex]x_{1}[/tex]) would be 2

Lets pick another y value from the graph.

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

So the x value corresponding to that ([tex]x_{2}[/tex]) would be 0

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

[tex]m=\frac{y_{1} -y_{2}}{x_{1}-x_{2}}[/tex]

=[tex]m=\frac{100-50}{2-0}[/tex]

=[tex]m=\frac{50}{2}[/tex]

=[tex]25[/tex]

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 [tex]25[/tex] units per second.