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

Question

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 .

BassanioGratiano · Answer

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)

aeropower · Answer

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.

the answer should be 103*(2^6).

82vkgmat · Answer

Same as above i think 103 should be 10^3. Answer = (2^6)*10^3 IMO.
Answer C.

thorinoakenshield · Answer

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
i.e. (2^6)(10^3) = ANSWER C

DesiGmat · Answer

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.

Bunuel · Answer

Yes, it should have been 10^3 instead of 103. Edited. Thank you.

PareshGmat · Answer

Answer = (C) (2^6)(10^3)

3 centuries have 6 half-centuries,

so population after 300 years = 2^6 * 10^3

Bunuel · Answer

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).

The correct answer is C.

Bunuel · Answer

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pacifist85 · Answer

I answered like this:

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 .

Madhavi1990 · Answer

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]

If this explanation was useful for you, please press kudos

ScottTargetTestPrep · Answer

Solution:

Three centuries, or 300 years, is 6 times 50 years. The population of Growthtown will double 6 times and become 10^3 x 2^6 in three centuries.

Answer: C

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

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