A grey squirrel population was introduced in a certain county of Great Britain 40 years ago. Biologists observe that the population doubles every 8 years, and now the population is 100,000.

(a) What was the initial size of the squirrel population?

Estimate the squirrel population 10 years from now.

sally1 Jul 10, 2014

#1**+5 **

Let the initial size be N_{0}.

After 8 years N = 2*N_{0}.

After 2*8 =16 years N = 2*2*N_{0} = 4N_{0}.

After 4*8 = 32 years N = 2*4*N_{0} = 8N_{0}.

After 8*8 = 64 years N = 2*8*N_{0} = 16N_{0}.

So it seems like the pattern is:

After n*8 years N = 2*n*N_{0}.

When n*8 = 40, we can see that n must be 5 (since 5*8 = 40) and we are told N = 100,000 so:

100000 = 2*5*N_{0}.

N_{0} = 100000/10 or N_{0} = 10,000

10 years from now is 50 years from the start, so n*8 = 50, n = 50/8

N = 2*(50/8)*10000 = 125,000

Alan Jul 10, 2014

#1**+5 **

Best Answer

Let the initial size be N_{0}.

After 8 years N = 2*N_{0}.

After 2*8 =16 years N = 2*2*N_{0} = 4N_{0}.

After 4*8 = 32 years N = 2*4*N_{0} = 8N_{0}.

After 8*8 = 64 years N = 2*8*N_{0} = 16N_{0}.

So it seems like the pattern is:

After n*8 years N = 2*n*N_{0}.

When n*8 = 40, we can see that n must be 5 (since 5*8 = 40) and we are told N = 100,000 so:

100000 = 2*5*N_{0}.

N_{0} = 100000/10 or N_{0} = 10,000

10 years from now is 50 years from the start, so n*8 = 50, n = 50/8

N = 2*(50/8)*10000 = 125,000

Alan Jul 10, 2014