Mathematical proof.

As previously posted: the family tree;

Generation: Population

0:1
1:2
2:4
3:8
4:16
5:32
6:64
7:128
8:256
9:512
10:1024
11:2048
12:4096

To discover our place within the population from the generation:

2^Generation

So then:

2^G=2^G

squareroot(2^G)=squareroot(2^G)

squareroot(2)=squareroot(2)

squareroot(2)/squareroot(2)

squareroot(1)=1

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Correction:

Population=2^G

G-Root(2^g)=2

First generation!

 

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r

A simplified equation for population growth is: \(N=N_o e^{rt}\).

These are true mathematical statements, but they don't tell you anything.

This is also true mathematically and also meaningless as far as populations go.

That is correct mathematically but is meaningless as far as populations go.

 

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Well how about the following(?):

G=Generation

G-Root(2^(G))/G-Root(2^(G))

 

I assume you mean: (G-Root(2^(G)))/(G-Root(2^(G))). That equals 1 which is not very revealing....

Or did you really mean: \(G - \frac{\sqrt(2^G)}{G}-\sqrt(2^G)\)

 

Looks to me that you are just using the *exponential function*, but that depends entirely on a steady rate of growth.

 

And assuming each couple only has one child.