Math Help Forum - View Single Post

Soroban · #3 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: . $r \;=\;0.340021838 \;\approx\;\boxed{34\%}$