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Scientist decided to do a study on the population growth of
rabbits. Inside a controlled environment, 1000 rabbits were
placed.
Six months later, there were 1000Z rabbits. At the beginning
of the 3rd year, there were roughly 2828Z rabbits, which was
4 times what the scientists placed in there at the beginning
of the 1st year.
If Z is a positive variable, how many rabbits would be there
at the beginning of the 11th year?
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Answer Posted / guest
At the beginning of the 11th year, there would be 1,024,000
rabbits.
At the beginning, there were 1000 rabbits. Also, there were
4000 rabbits at the beginning of third year which is equal
to 2828Z. Thus, Z = 4000/2828 i.e. 1.414 (the square root of 2)
Note that 2828Z can be represented as 2000*Z*Z (Z=1.414),
which can be further simplified as 1000*Z*Z*Z*Z
Also, it is given that at the end of 6 months, there were
1000Z rabbits.
It is clear that the population growth is 1.414 times every
six months i.e. 2 times every year. After N years, the
population would be 1000*(Z^(2N)) i.e. 1000*(2^N)
Thus, at the beginning of the 11th year (i.e. after 10
years), there would be 1000*(2^10) i.e. 1,024,000 rabbits.
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