Question

I just want to go to sleep but I need the answer to this question

Answer 1

The average rate of change of a function f(x) from x1 to x2 is given by:

`(f(x_2)-f(x_1))/(x_2-x_1)`

In this case we need the first three seconds so x1=0 and x2=3.

Calculate the values of the function at x=0 and x=3 to get:

f(0)=150 and f(3)=0.

Substitute these values into the formula for average rate of change:

`\begin{gathered} (f(3)-f(0))/(3-0) \\ =(0-150)/(3) \\ =(-150)/(3) \\ =-50 \end{gathered}`

Hence the avearage rate of change of the function for the first three seconds is -50.

Note that the negative sign shows that the function is decreasing in the time interval (first three seconds).