Need help

theduck1980 · #1 $Old$ August 9th, 2008, 04:34 PM

I need a formula for the following - hopefully this isn't much of a challenge, but I can't figure it out! lol

It's regarding a peice i'm doing on our population since the beginning(well christian beginning anyway)

Population went from two -> 6.83 billion(current) The christians believe the earth is only around 6,000 yrs old... so working on the average generation lasting 80yrs, thats 75 generations since Adam & Eve

I want to find out what percentage or number each generation has to grow in order to reach our current population.

With the data, I hope to estimate the total population of people who have lived & died + the current population since adam & eve...

janvdl · #2 $Old$ August 9th, 2008, 05:48 PM

Quote:

Originally Posted by theduck1980 $View Post$

I need a formula for the following - hopefully this isn't much of a challenge, but I can't figure it out! lol

It's regarding a peice i'm doing on our population since the beginning(well christian beginning anyway)

Population went from two -> 6.83 billion(current) The christians believe the earth is only around 6,000 yrs old... so working on the average generation lasting 80yrs, thats 75 generations since Adam & Eve

I want to find out what percentage or number each generation has to grow in order to reach our current population.

With the data, I hope to estimate the total population of people who have lived & died + the current population since adam & eve...

I think the compound interest formula would suffice to find the percentage rate. Although its a very crude method you are using, since few people in old times saw 60, nevermind 80. On a side note, the creation was done in 7 phases not 7 days, and if you read the Bible you will also note that the seventh day has not yet passed, so while mankind may hav existed for only 6000 years, the earth has not.

Soroban · #3 $Old$ August 9th, 2008, 08:49 PM

Hello, theduck1980!

jandvl is absolutely correct . . .

Quote:

Population went from 2 to 6.83 billion (current).
The Christians believe the earth is only around 6,000 years old.
So working on an average generation of 80 yrs, that's 75 generations since Adam & Eve.

I want to find out what percentage or number each generation has to grow
in order to reach our current population.

We have the function: . $P(n) \;=\;P_o(1+r)^n$

. . where: . $\begin{array}{ccc}P_o &=& \text{population at }n=0 \\ r &=& \text{\% increase per generation} \\ n &=& \text{number of generations} \end{array}$

We are told: .When $n = 0,\;P = 2$

. . We have: . $2 \:=\:P_o(1+r)^0 \quad\Rightarrow\quad P_o = 2$

The function (so far) is: . $P \;=\;2(1+r)^n$

We are told: .When $n = 75,\;P = 6,830,000,000$

. . We have: . $6,830,000,000 \;=\;2(1+r)^{75} \quad\Rightarrow\quad (1+r)^{75} \;=\;3,415,000,000$

Take logs: . $\ln(1+r)^{75} \;=\;\ln(3,415,000,000) \quad\Rightarrow\quad 75\!\cdot\!\ln(1+r) \;=\;\ln(3,415,000,000)$

. . $\ln(1+r) \;=\;\frac{\ln(3,415,000,000)}{75} \;=\;0.292685911$

Then: . $1 + r \;=\;e^{0.292685911} \;=\:1.340021838$

Therefore: . $r \;=\;0.340021838 \;\approx\;\boxed{34\%}$