We have to calculate the average rate of change of the function f(x) in the first two seconds.
As the function is a line, the rate of change is constant and is equal to the slope, as the slope is defined as the quotient of the variation of y=f(x) and the variation of x.
Taking two point (x=0 and x=2), we will calculate the rate of change:
When x = 0, f(0) = 50.
When x = 2, f(2) = 100.
Then, we can calculate the slope (or rate of change) as:
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{100-50}{2-0}=\frac{50}{2}=25[/tex]
The average rate of change between 0 and 2 is 25.
