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kumpel [21]
3 years ago
11

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 l

onger 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
Mathematics
1 answer:
erma4kov [3.2K]3 years ago
3 0

Answer:

(E). 19

Step-by-step explanation:

Let original population of each colony be P.

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:

P(2)^x

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

The total population of both the colonies at that point will be P(2)^{19}+P(2)^{19}=2P(2)^{19}=P(2)^{20} 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.

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(b)1/12

Step-by-step explanation:

Given that the cubes are numbered from 1 to 6.

The possible outcomes are:

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(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

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Total number of possible Outcomes=36

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Probability that the sum of the number cubes is 7.

The outcomes that sums up to 7 are:

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Number of outcomes=6

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P(sum of the number cubes is 7)=6/36=1/6

<u>Part B</u>

The sum of the number cubes is less than 4.

Outcomes in which the sum is less than 4 are:

(1,1) (1,2) (2,1)

Number of outcomes=3

Therefore:

P(sum of the number cubes is less than 4)=3/36=1/12

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