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

We have been given that a certain bacteria colony doubles in size every day, so bacteria colony is growing exponentially. After x days, the population of bacteria would be:

[tex]P(2)^x[/tex]

The population after 19 days will be [tex]P(2)^{19}[/tex] for each colony.

The total population of both the colonies at that point will be [tex]P(2)^{19}+P(2)^{19}=2P(2)^{19}=P(2)^{20}[/tex] which is what the habitat's limit is.

Therefore, it will take 19 days for two bacteria colonies to reach the habitat's limit and option E is the correct choice.

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

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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