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.

Question

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

Enter your answer in logarithmic form. For example, if your answer is log42(53), enter it like this: log_42(53)

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

Answer 1

Is the answer log_2(50)?

Answer 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.

Answer 3

Thank you!