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100pts: Prove that the Fibonacci sequence is an example of exponential growth

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Answer:

It is an exponential growth.

Explanation:

took this on edge

User Josedlujan
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1 vote

Answer:

It is an exponential growth.

If we keep adding the most recent 2 numbers (the Fibonacci sequence)

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89

we will see that the last number divided by the previous number (for example 89 / 55 = 1.6181818182 approaches a limit of 1.6180339 which is known as the phi ratio.

Basically, we are looking for a number with a rate of growth equal to itself.

Phi is an irrational number equal to [1 + sq root (5) / 2]

which equals 1.6180339...

Then we can say that the NEXT Fibonacci number equals the

PREVIOUS Fibonacci number times "phi".

Next number = previous number * phi

Explanation:

User Robert Petz
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