# A certain population of rabbits is doubling its population every 2 months. The original population started with only 20 rabbits. A biologist studying the population found that the equation 1000=20(2)^t shows how many months, t, it will take before there are 1000 rabbits in the population.

How many months will it take for the population to reach 1000 rabbits?

***I have no clue what the answer is, let alone how to solve this. Can I get some help please. Thank you.***

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2. First of all the equation should be
1000 = 20(2)^(t/2)
divide both sides by 20
50 = 2^(t/2)
take log of both sides and use log rules
(t/2)log2 = log50
t/2 = log50/log2 , which would be log2 50
t/2 = 5.64..
t = 11.29 months

check:
after 2 months there would be 40
after 4 months there would be 80
after 6 months there would be 160
after 8 months there would be 320
after 10 months there would be 640
after 12 months there would be 1280 , my answer of 11.29 months for 1000 rabbits looks very
reasonable.

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3. Thank you!

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