There are 52 white keys on a piano.
The frequency of each key is the number of vibrations per second the
key's string makes.
Is this relation a function? If not, explain why.
If so, predict an equation that models the data.
Key Position 
1 
8 
15 
22 
29 
36 
43 
Frequency 
27.5 
55 
110 
220 
440 
880 
1760 

Source: Bellman, A. et. al, (no date) Algebra. Nedham, MA:
PrenticeHall.
In order to find whether
or not the relation is a function and predict an equation that models
the data we can use a spreadsheet. (Click
here for the spreadsheet).
A function is defined as
a rule of matching elements of two sets of numbers in which an input
value from the first set has only one output value in the second set. We
see that this relationship is a function because each element in the
range (y) is assigned to a unique value in the domain. We also see that
the equation that models the data in this case is
To extend this problem,
we can find the frequency of all 52 keys using the equation y =
24.907e^{0.099x} by using a spreadsheet.
Click here for spreadsheet.