Exponential models of population growth question.

[LJay]

A certain species of bird was introduced in a certain country 25yrs ago. Biologists observe that the population doubles every 10 years, and now the population is 13,000.

Using this model..

n(t) = (n0) * (e^(rt))

where:

n(t) = population at time t
n0 = initial size of the population
r = relative rate of growth (expressed as a proportion of the population)
t = time


a. What was the initial size of the bird population?
b. Estimate the bird population 5yrs from now.

I set A up as:

13,000 = n0 * e^(.2*25)

n0 = (13,000)/(e^(.2*25))
n0 = 87.59331099

not sure if i'm doing this right
i used (.2) as r because 200% every 10 years = 20% every year?

i got 35,337.6 for B by substituting (30) for t using:

n(30) = 87.59331099 * e^(.2*30)

5 years from now = 30 years from initial time?

doesnt look right to me
any help would be appreciated
be gentle

 

[tkhunny]

Your first clue should be e^(0.20 * 10) <> 2. Something seriously wrong with your model.

You need e^(10k) = 2. Solve for k. Once you have a handle on this solution, THEN you can start writing them cold.

 

[LJay]

thanks a lot TK
i'm math retarded

 

[Denis]

thanks a lot TK
i'm math retarded

Now now Jay, none of that :shock:

Redeem yourself:
at rate of 7% compounded annually, how long does it take $1 to accumulate to $3 ?

 

[LJay]

thanks a lot TK
i'm math retarded

Now now Jay, none of that :shock:

Redeem yourself:
at rate of 7% compounded annually, how long does it take $1 to accumulate to $3 ?

16.2376 yrs?

 

[Denis]

Right on :wink: