we know that
the volume of a rectangular prism is equal to
where
L is the length of the box
W is the width of the box
H is is the height of the box
in this problem we have
<u>Find the length of the box</u>
Using a graph tool-------> we will determine the roots of the equation of volume
see the attached figure
the roots are
so
therefore
<u>the answer is</u>
the length of the box is equal to
Part A:
The average rate of change refers to a function's slope. Thus, we are going to need to use the slope formula, which is:
You can see that we are given the x-values for our interval, but we are not given the y-values, which means that we will need to find them ourselves. Remember that the y-values of functions refers to the outputs of the function, so to find the y-values simply use your given x-value in the function and observe the result:
Now, let's find the slopes for each of the sections of the function:
<u>Section A</u>
<u>Section B</u>
Part B:
In this case, we can find how many times greater the rate of change in Section B is by dividing the slopes together.
It is 25 times greater. This is because is an exponential growth function, which grows faster and faster as the x-values get higher and higher. This is unlike a linear function which grows or declines at a constant rate.