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A certain bacteria colony doubles in size every day for 20 [#permalink]

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30 Mar 2012, 02:35

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43% (01:23) wrong based on 110 sessions

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A certain bacteria colony doubles in size every day for 20 days, a which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?

Re: A certain bacteria colony doubles in size every day for 20 [#permalink]

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30 Mar 2012, 03:06

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Case 1: Consider the bacteria num to be B. As it doubles every day, number of bacteria at the end of each day would be Day 1 – B Day 2 – 2B Day 3 – 4B Day 4 – 8B . . . Day 20 – 2^19 B It can be implied that the capacity of the habitat is 2^19 B.

Case 2: There are 2 bacteria which keep doubling every day. So, the count would be Day 1 – 2B Day 2 – 4B Day 3 – 8B . . . Day 18 – 2^18 B Day 19 – 2^19 B --> this is the point where the habitat is filled to its capacity. Hence, 19 is the answer

A certain bacteria colony doubles in size every day for 20 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?

A. 6.33 B. 7.5 C. 10 D. 15 E. 19

If there is one bacteria colony, then it will reach the limit of its habitat in 20 days.

If there are two bacteria colonies, then in order to reach the limit of habitat they would need to double one time less than in case with one colony. Thus colonies need to double 19 times.

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