Q:

population growth?

i've heard that if in a population each pair has 4 children, then after 4 generations it's a 1600% increase.. 
I suppose after 1 generation it is 200%, and each successive generation is 200%, and they multiply  200%^4  But, if I try it out with figures like this, I never get 1600%
suppose a population of 10
g  g1 g2 g3  g4
10 20 40 80  160

So each generation is double the previous, and from the start of g, population of 10, each of 4 generations g1-g4 have 4 children.
10+20+40+80+160=310
(310-10)/10 = 3000% 
Not 1600%
Howcome i'm not getting 1600%?

A:

First, you need to be careful with the terminology: if you have a quantity $X$, and you go to quantity $Y\gt X$, then the percentage of increase is 
$$\frac{100(Y-X)}{X}.$$
For example, if you start with $X=10$, and double to $Y=20$, then the percentage of increase is 100%; however, $Y$ is "200%" of the original. And therein probably lies the problem.
A "1600%" increase would mean that if you start with 10, then the difference between the final total and 10 is $160$, so the final total will be $170$ (the increase plus the original); so the final total will be 17 times the original. On the other hand, if we mean that the total population at the end will be 1600% the original population, then the percentage of increase is "only" 1500%. 
Now, for your problem: if you have a population of $P$, and we assume everyone in the population breeds, then you get $4$ offspring for every $2$ people, that means that in addition to the original $P$, you will have $4\left(\frac{P}{2}\right) = 2P$ offspring in the next generation.
If we assume that each generation "dies" after the offspring is born and grows to maturity (so each generation has only the number of individuals that were born in the previous generation), then you have the recurrence
$$P = P_0,\qquad P_{n+1}=2P_n$$
each generation doubles in size from the previous one. You start with $10$, then the next generation has $20$, then $40$, then $80$; if you mean to go to the "next" one after that, it's $160$.
That's an increase of $150$, or 1500%. However, $160$ is of course 16 times the original population, and is 1600% of the original population, probably what was meant.
If the original population remains alive (and continues to breed) throughout, then we have the recurrence
$$P = P_0,\qquad P_{n+1} = P_n + 2P_n = 3P_n$$
so each generation is three times as big as the previous one.
If we start with $10$, after the next generation is born we have $30$, then after the next generation is born we have $90$, and after the next generation is born, $270$. that's a total increase of $260$, and a growth of 2600%. If we mean the generation after that, then you would have $810$ individuals, for a total increase of 8000%, and a final population which is 8100% the original one.

