SOLUTION: Find an algebraic relationship between the following: n----------z 0---------64 1----------96 2----------48 3----------8

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Question 1003565: Find an algebraic relationship between the following:
n----------z
0---------64
1----------96
2----------48
3----------8
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There are many possible algebraic relationships between n and z .
The question is: what is the answer your teacher expects?

64=2%5E6=2%5E6%2A1=2%5E6%2A3%5E0
96=2%5E5%2A3=2%5E6%2A3%5E1
48=2%5E6%2A3=2%5E4%2A3%5E1
8=2%5E3=2%5E3%2A1=2%5E3%2A3%5E0
All the z values are of the form 2%5Ex%2A3%5Ey
with system%28x=6=n%2C+y=n%283-n%29%2F2%29 .
So, highlight%28z=2%5E%286-n%29%2A3%5E%28n%283-n%29%2F2%29%29 works as an algebraic relationship between n and z .

With n points, you can always fit them to a polynomial function of degree n-1 , so
with 4 points a cubic polynomial would work.
In this case, highlight%28z=%2844%2F3%29n%5E3-84n%5E2%2B%28304%2F3%29n%2B64%29%29 also works.

I could try to work out coefficients for other algebraic relationships,
but it's past my bedtime, and I am having trouble reading your teacher's mind.