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# The population of Growthtown doubles every 50 years. If the number of

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Math Expert
Joined: 02 Sep 2009
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The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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11 Jan 2015, 12:35
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76% (01:13) correct 24% (01:14) wrong based on 123 sessions

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The population of Growthtown doubles every 50 years. If the number of people in Growthtown is currently 10^3 people, what will its population be in three centuries?

(A) 3(10^3)
(B) 6(10^3)
(C) (2^6)(10^3)
(D) (10^6)(10^3)
(E) (10^3)^6

Kudos for a correct solution.

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Re: The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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11 Jan 2015, 14:31
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Hi Bunuel,

I think there might be a typo in your question. Do you mean 10^3 instead of 103?

If so I pick C.

If the town doubles every 50 years then within 3 centuries the town will double 6 times.

(2^6)(10^3)
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Re: The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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11 Jan 2015, 19:01
Agreed I think there may be a typo.

But overall each period the city grows at 2^period.

It doubles at 50 years, 3 centuries is 300 years or 6 periods.

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Re: The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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11 Jan 2015, 20:09
Same as above i think 103 should be 10^3. Answer = (2^6)*10^3 IMO.
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Re: The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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11 Jan 2015, 20:47
I agree with others. There is a typo in the problem. Population should be 10^3.

Population doubles every 50 years.
After 300 years, we have 6 sets of 50.
Hence, the doubling rate for 3 centuries = 2^6
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Re: The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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11 Jan 2015, 23:06
It will be a GP with a common difference of 2

3 centenuries = 300 ---> 50*6
It doubles after every 50 years...

So after 3 centuries the population will be (2^6) * 103

Considering there is a typo...
going with option C.
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Re: The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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12 Jan 2015, 00:44
BassanioGratiano wrote:
Hi Bunuel,

I think there might be a typo in your question. Do you mean 10^3 instead of 103?

If so I pick C.

If the town doubles every 50 years then within 3 centuries the town will double 6 times.

(2^6)(10^3)

Yes, it should have been 10^3 instead of 103. Edited. Thank you.
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Re: The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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14 Jan 2015, 03:02

3 centuries have 6 half-centuries,

so population after 300 years$$= 2^6 * 10^3$$
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Re: The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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19 Jan 2015, 02:31
Bunuel wrote:
The population of Growthtown doubles every 50 years. If the number of people in Growthtown is currently 10^3 people, what will its population be in three centuries?

(A) 3(10^3)
(B) 6(10^3)
(C) (2^6)(10^3)
(D) (10^6)(10^3)
(E) (10^3)^6

Kudos for a correct solution.

OFFICIAL SOLUTION:

If the population doubles every 50 years, in 3 centuries (300 years) the population will double 6 times. You can express this value as 2^6. The 2 represents the doubling event and the 6 represents that it happens 6 times. So multiply the 10^3 people by 2^6 to find total population. You don’t have to multiply the value because answer C states it simply as (2^6)(10^3).

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Re: The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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19 Jan 2015, 02:32
Bunuel wrote:
Bunuel wrote:
The population of Growthtown doubles every 50 years. If the number of people in Growthtown is currently 10^3 people, what will its population be in three centuries?

(A) 3(10^3)
(B) 6(10^3)
(C) (2^6)(10^3)
(D) (10^6)(10^3)
(E) (10^3)^6

Kudos for a correct solution.

OFFICIAL SOLUTION:

If the population doubles every 50 years, in 3 centuries (300 years) the population will double 6 times. You can express this value as 2^6. The 2 represents the doubling event and the 6 represents that it happens 6 times. So multiply the 10^3 people by 2^6 to find total population. You don’t have to multiply the value because answer C states it simply as (2^6)(10^3).

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The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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28 Feb 2015, 06:53

Now: 10^3 = 2^3 * 5^3
+50 years: 2 * 10^3 = 2 * 2^3 * 5^3 = 2^4 * 5^3, so we only add 1 to the power of 2.
+50 years: 2^5 * 5^3
+50 years: 2^6 * 5^3
+50 years: 2^7 * 5^3
+50 years: 2^8 * 5^3
+50 years: 2^9 * 5^3

Answer C is 2^6 * 10 ^3 = 2^6 * 2^3 * 5*3 = 2^9 *5^3, which is what we found just above. So ANS C.
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Re: The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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06 Dec 2017, 10:53
if it double every 50 years, it is four times for that 100
so year 1 -->10^3
after 100 years --> 4(10)^3
after 200 years --> 4*4(10)^3
after 300 years --> 16*4(10)^3

so answer is 2^6 (10)^3 [64 = 2^6]

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Re: The population of Growthtown doubles every 50 years. If the number of  [#permalink]

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09 Dec 2019, 13:03
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Re: The population of Growthtown doubles every 50 years. If the number of   [#permalink] 09 Dec 2019, 13:03
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