## Question on Population Growth

**Moderators:** Leonid, amiradm, BioTeam

### Question on Population Growth

Hi, not sure if somebody is able to help me with this.

Consider this: a population that starts with 2 individuals, has a growth rate of 0.5. There is a carrying capacity of 500 individuals. How long will it take this limited population to reach its carrying capacity?

Consider this: a population that starts with 2 individuals, has a growth rate of 0.5. There is a carrying capacity of 500 individuals. How long will it take this limited population to reach its carrying capacity?

I would feel more optimistic about a bright future for man if he spent less time proving that he can outwit nature and more time tasting her sweetness and respecting her seniority. ~ E. B. White

this is the exact question verbatim. there are no units for the growth rate - normally it's expressed as percentage.

I would feel more optimistic about a bright future for man if he spent less time proving that he can outwit nature and more time tasting her sweetness and respecting her seniority. ~ E. B. White

So, the inital population is 2. When they spawn another generation, you multiply n (2, in this case) by 1.5, which gets you 3 individuals. After the first generation of mating, you'll have 3 individuals, which will be your new n when you calculate generation 3. Keep compounding n for each generation, and keep track of how many generations you've gone through.

Once you've hit 500 individuals, you'll stop computing, since the population won't increase anymore. The number of generations the population has produced will be how long it took (measured in generations) for your population to reach carrying capacity.

There's probably an equation that you can use to compound each generation automatically using calculus, but I'm too tired to figure one out right now. So while it may not be too terribly fast, the above method should give you the right answer.

- AstusAleator
- King Cobra
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