The Population of the Bacteria Colony Doubles Every Day. If It was Started 9 Days Ago with 2 Bacteria and each Bacteria Lives for 12 Days, how Large is the Colony Today?

Question: The population of the bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today? 

1. 512
2. 768
3. 1024
4. 2048
5. 4096

“The population of the bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today? ”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

As given in the question, Population doubles every day. If the population started one day age, this means it would be \(2^2\) today.

So we can say that if the population started N days ago, then today it will be \(2^{n+1}\)

Time Elapsed | Bacteria

9 days ago \(\rightarrow \) 2

8 days ago \(\rightarrow \) 4

7 days ago \(\rightarrow \) 8

6 days ago \(\rightarrow \) 16

5 days ago \(\rightarrow \) 32

4 days ago \(\rightarrow \) 64

3 days ago \(\rightarrow \) 128

2 days ago \(\rightarrow \) 256

1 day ago \(\rightarrow \) 512

So, we can say that today the population size is \(2^{10}\) = 1024

Correct Answer: C

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