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# Using Functions with Variation

I have a story problem that involves using variation and functions, and I don't even know where to begin or how to read this problem. Could you walk through setting it up and solving it please! Thank you very much!

-Megan

(Problem 42 is an example of the golden ratio, or phi, a proportionality constant that appears in nature. The numerical approximate value of phi is 1.618. From http://www.goldenratio.net.

42. Human Anatomy
Each section of your index finger, from the tip to the base of the wrist, in larger than the preceding one by about the golden (Fibonacci) ratio. Find an equation that represents the ratio of each section of your finger related to the previous one if one section is 8 units long and the next section is 5 units long.

Megan,

The question has a LOT of extra fluff in this question that may be tripping you up.  The last sentence is the only one that holds any true meaning in regards to finding an answer.

Essentially, it is asking you to create a linear equation that will tell you the next number in the sequence.  If we start at 8 and go to 5, what is the ratio of change? *Answer* 5/8.  If this were geometry you could consider this your slope.  Building an equation from this, your next predicted value (y) should be five eighths (5/8) of your previous value (x).  Thus the equation y=(5/8)x.  Alternatively, this could be written as y=(1.6)x.

Is that one of your options?

-Sam