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

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- May 14th 2009, 10:37 PMJoker37rabbit 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 PMpickslides
I would use the following population model. There are others you could consider

$\displaystyle P = P_0R^t$

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

In your case

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

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

you should be fine from here... - May 16th 2009, 08:14 PMJoker37
- May 16th 2009, 09:26 PMmr fantastic
- May 16th 2009, 09:41 PMbianca
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 PMpickslides
- May 18th 2009, 02:43 PMe^(i*pi)
I learnt mine as $\displaystyle P=P_0(1+x)^t$ 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