How can population growth be modeled using a simple equation?

[rock.freak667]

Homework Statement

In a model for the growth of a population,p_n is the number of individuals in the population at the end of n years. Initially, the population consists of 1000 individuals.

In each year, the population increases by 20% and on Dec.31st, 100 individuals leave the population.

a)Calculate p_1 \ and \ p_2
b)Write down an equation connecting p_{n+1} \ and \ p_n

Homework Equations

None

The Attempt at a Solution

Well at the initial time. p=1000

so at the end of the first year it would just be 1000-100
so that p_1=900

At the start of the next year the new population size is \frac{120}{100}*900=1080
so then simply p_2=1080-100=980

are these values correct?
If my answers are correct, then for part b) should it just simply be
p_{n+1}=(1.2*p_n)-100

 

[Dick]

I think you want to grow the population by 20% first, then subtract 100. As you wrote in b), but didn't do in a).

 

[rock.freak667]

But in part a) doesn't initially mean that it is at the start of the calendar year and the population growth should be valid for the year after?

 

[Dick]

I would say Dec 31 is at the end of the year, so you would start with 1000 on Jan 1 of the first year. I was just trying to make b) applicable to p0=1000. It's roughly the same problem either way, in one case you start with 1000 on Dec 31, in the other with 1000 on Jan 1.

 

[rock.freak667]

so then the formula for P_n and P_n+1 is correct?

 

[HallsofIvy]

Yes, it is.