Guesstimate: Population question

Question

Hi, can anyone suggest a sound approach to solve this guesstimate question:

If a male and a female goat are put on a deserted island that has plenty of food and water on it, what would be the island’s goat population after ten years?

Thanks!

Answer 1

Hi,

Assume how much time it takes the population to double (let's say 2 years as they need 2 kids). So the population will double 5 times in 10 years
Population in 10 years = 2*2^5

Best

Answer 2

Consider the following:
1. Given that you don't know how much time goat's pregnancy takes, knowing it is a mammal you should know it wouldn't be less than a couple of months, and probably not much more than 1 year. Assuming 1-2 (so an average of 1.5) pregnancy per a year per a female goat is fair.
2. We start with one female goat so year one is 1.5 *1, year to could be assumed as 1.5 * 2
(we round up the7.5 = .5 probability of having a female born times 1.5) and we add the number of males, which is always assumed to be the same num of females (so 2); total 2*1.5=3+2=5
3. Continue: 5+(1.5*2.5)+2.5..... n+(1.5* n/2)+n/2... 10+(1.5*5)+5

The number itself does not matter in this case, as long as you are not making an order of magnitude mistake. What matters is that your express explicitly your assumptions, flash out the model you are thinking of and reason through it. Good luck!

Check yourself:
Goat's pregnancy is indeed 5 months. Life expectation is 15-18 years (so irrelevant here).
https://articles.extension.org/pages/19720/goat-reproduction-puberty-and-sexual-maturity