A grey squirrel population was introduced in a certain county of Great Britain

label Algebra
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schedule 1 Day
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35 years ago. Biologists observe that the population doubles every 7 years, and now the population is 120,000.

(a) What was the initial size of the squirrel population?
Apr 17th, 2015

Let Initial Population = X 

Since the population doubles after every 7 years 

Population after 7 years = 2 * X 

Population after 14 (7 *2)  years = 2 * (2 * X) = 4 * X 

Population after 21 (7 *3) years = 2 * (4*X) = 8 *X

Population after 28 (7*4) years = 2 * (8*X) = 16 * X 

Population after 35 (7*5)  years = 2 * (16*X) = 32 * X 

The relation is 

Population after 7*n  years = (2^n) * X

After 35 years population = 120,000 = 32 * X 

solving for X we get 

X = 120000 / 32 = 3750 

Initial population was 3750 (Answer) 

Apr 17th, 2015

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Apr 17th, 2015
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Apr 17th, 2015
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