## Question on Population Growth

Debate and discussion of any biological questions not pertaining to a particular topic.

bionewbie
Coral
Posts: 113
Joined: Sun Nov 07, 2004 9:54 pm

### 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?
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

2810712
King Cobra
Posts: 697
Joined: Thu Jan 20, 2005 12:19 pm
what are the units of 0.5 [ growth rate] used here...?

bionewbie
Coral
Posts: 113
Joined: Sun Nov 07, 2004 9:54 pm
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

Khaiy
Coral
Posts: 158
Joined: Tue Feb 28, 2006 2:37 am
So can we assume that the population increases by .5 individuals times the total population per generation?

bionewbie
Coral
Posts: 113
Joined: Sun Nov 07, 2004 9:54 pm
yes, the trouble i have is incorporating the 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

Khaiy
Coral
Posts: 158
Joined: Tue Feb 28, 2006 2:37 am
Well, the carrying capacity basically tells you when to stop. Let's designate the number of individuals as "n". Multiply n by 1.5 to get the number of individuals from generation one, plus the number of individuals made in generation two.

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
Posts: 1039
Joined: Tue Jan 24, 2006 8:51 pm
Location: Oregon, USA
well according to Khaiys method and some basic arithmetic I got 1.5^n=250. You just need to find n... Good luck . It's something like 13.6179...? Too tired to try to remember the calculus
What did the parasitic Candiru fish say when it finally found a host? - - "Urethra!!"