# rabbit population

• May 14th 2009, 10:37 PM
Joker37
rabbit population
If a population of rabbits, originally 15 000, is increasing at 3% per annum, find the population after 15 years have passed.
• May 14th 2009, 11:21 PM
pickslides
I would use the following population model. There are others you could consider

$P = P_0R^t$

where P = population, $P_0$ = Initial Population, R = Growth Rate and t = time in years

$P_0$ = 15,000, R = 3% (increasing) and t = 15

therefore $P = 15,000(1.03)^{15}$

you should be fine from here...
• May 16th 2009, 08:14 PM
Joker37
Quote:

Originally Posted by pickslides
I would use the following population model. There are others you could consider

Hmmm...no, I haven't gone through the population model thing. Does anyone know of any other ways to solve this? Perhaps involving linear recursion relationships?
• May 16th 2009, 09:26 PM
mr fantastic
Quote:

Originally Posted by Joker37
If a population of rabbits, originally 15 000, is increasing at 3% per annum, find the population after 15 years have passed.

Quote:

Originally Posted by Joker37
Hmmm...no, I haven't gone through the population model thing. Does anyone know of any other ways to solve this? Perhaps involving linear recursion relationships?

15,000 + 3% of 15,000 = 15,000 + (0.03)(15,000) = 15,000 + 540 = 15,450.

15,450 + 3% of 15,450 = 15,450 + (0.03)(15,450) = 15,450 + 463.5 = 15,913.5

etc etc.
• May 16th 2009, 09:41 PM
bianca
You have to think like if you where figuring out saving account interest.
15000____100%
?????_____3%

15000 times 3% divide it by 100

45000 divide by 100 = 450

At the end of the first year you have 15450 rabbits. then 15450 is your new 100% and you start all over until 15 years have pass.
• May 18th 2009, 02:36 PM
pickslides
Quote:

Originally Posted by Joker37
Hmmm...no, I haven't gone through the population model thing. Does anyone know of any other ways to solve this? Perhaps involving linear recursion relationships?

I think the model I have given you is probably the most easiest to understand. My advice would be to get your head around this one first of all and then look into exploring more complex models. (Cool)
• May 18th 2009, 02:43 PM
e^(i*pi)
Quote:

Originally Posted by Joker37
If a population of rabbits, originally 15 000, is increasing at 3% per annum, find the population after 15 years have passed.

I learnt mine as $P=P_0(1+x)^t$ which is in essence the same as pickslides' method except he has R where I have (1+x).

The exponential model is probably the simplest method.

Of course this is based on the assumption that the growth can be modelled by exponential growth and that there are no reasons for numbers to decline