A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 13,000. What was the initial size of the bird population?

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Answer 1 · 2016-12-30T20:12:21

#2298#

The population is modelled by the formula:

#P(t) = p_0*2^(t/10)#

where #p_0# is the initial population and #t# the time in years.

So we have:

#13000 = P(25) = p_0*2^(25/10) = p_0*2^(5/2) = 4sqrt(2)p_0#

So the initial population is:

#p_0 = 13000/(4sqrt(2)) = 13000/8sqrt(2) = 1625sqrt(2) ~~ 2298#