Question

The graph below plots a function f(x): 220 200 180 160 140 120 100 BO If x represents time, the average rate of charge of the function for in the first two seconds is___________.

Answer 1

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:

`m=(f(x_2)-f(x_1))/(x_2-x_1)=(100-50)/(2-0)=(50)/(2)=25`

The average rate of change between 0 and 2 is 25.