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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.
 Jul 10, 2014

Best Answer 

 #1
avatar+33273 
+5

Let the initial size be N0.

After 8 years N = 2*N0.

After 2*8 =16 years N = 2*2*N0 = 4N0.

After 4*8 = 32 years N = 2*4*N0 = 8N0.

After 8*8 = 64 years N = 2*8*N0 = 16N0.

So it seems like the pattern is:

After n*8 years N = 2*n*N0.

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*N0.

N0 = 100000/10 or N0 = 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

 Jul 10, 2014
 #1
avatar+33273 
+5
Best Answer

Let the initial size be N0.

After 8 years N = 2*N0.

After 2*8 =16 years N = 2*2*N0 = 4N0.

After 4*8 = 32 years N = 2*4*N0 = 8N0.

After 8*8 = 64 years N = 2*8*N0 = 16N0.

So it seems like the pattern is:

After n*8 years N = 2*n*N0.

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*N0.

N0 = 100000/10 or N0 = 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

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