Answer:
h = 9n
Step-by-step explanation:
Since h (height) is a function of number of DVDs then we can express in the form of:
[tex]\displaystyle{h = an+b}[/tex]
where h is height, a is rate of change, n is number of DVD and b is the initial height which of course is 0 (proportional). Henceforth, we will be with the equation:
[tex]\displaystyle{h = an}[/tex]
Next, we will be finding the rate of change of how much the dependent values change with respect to the independent values. That can be expressed as:
[tex]\displaystyle{a = \dfrac{h_2 - h_1}{n_2-n_1} = \dfrac{\Delta h}{\Delta n}}[/tex]
delta means "change of/in"
We will pick [tex]\displaystyle{(n_1,h_1) = (2,18)}[/tex] and [tex]\displaystyle{(n_2, h_2) = (3,27)}[/tex]. Therefore, substitute in the rate of change formula:
[tex]\displaystyle{a = \dfrac{27-18}{3-2}}\\\\\displaystyle{a = \dfrac{9}{1}}\\\\\displaystyle{a = 9}[/tex]
Therefore, the rate of change is 9. Substitute a = 9 in and therefore, the equation for the table is:
[tex]\displaystyle{h = 9n}[/tex]
