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At the start of an experiment, a certain population consisted of \(3\) animals. At the end of each month after the start

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by Vincen » Thu Nov 26, 2020 12:23 pm

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At the start of an experiment, a certain population consisted of \(3\) animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of \(10\) months?

(A) \(2^3\)
(B) \(3^2\)
(C) \(2(3^{10})\)
(D) \(3(2^{10})\)
(E) \(3(10^2)\)

Answer: D

Source: Official Guide
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Source: — Problem Solving |

Vincen wrote:
Thu Nov 26, 2020 12:23 pm
At the start of an experiment, a certain population consisted of \(3\) animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of \(10\) months?

(A) \(2^3\)
(B) \(3^2\)
(C) \(2(3^{10})\)
(D) \(3(2^{10})\)
(E) \(3(10^2)\)

Answer: D

Source: Official Guide
This is a great candidate for creating a growth table

ELAPSED TIME (in months) | NUMBER OF ANIMALS
0 | 3
1 | (3)(2) animals [since the population doubles each month]
2 | (3)(2)(2) animals
3 | (3)(2)(2)(2) animals
4 | (3)(2)(2)(2)(2) animals
.
.
.
We can see the pattern and recognize that, at the end of month 10, we'll have the product of one 3 and ten 2's.
.
.
10 | (3)(2)^10

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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