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03 Jun 2018, 12:43
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D
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A cockroach population doubles every 3 days. In 30 days, by what percent would a cockroach population increase?
(A) 900%
(B) 1,000%
(C) 9,999%
(D) 102,300%
(E) 102,400%
(A) 900%
(B) 1,000%
(C) 9,999%
(D) 102,300%
(E) 102,400%
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Expert reply
03 Jun 2018, 13:35
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Bunuel
A cockroach population doubles every 3 days. In 30 days, by what percent would a cockroach population increase?
(A) 900%
(B) 1,000%
(C) 9,999%
(D) 102,300%
(E) 102,400%
(A) 900%
(B) 1,000%
(C) 9,999%
(D) 102,300%
(E) 102,400%
Assume cockroach population now is x
Now =x
Day 3 = 2x
Day 6 = 4x
Day 9 = 8x
Day 12 = 16x
Day 15 = 32x
Day 18 = 64x
Day 21 = 128x
Day 24 = 256x
Day 27 = 512x
Day 30 = 1024x
% increase = \(\frac{(New - Old)}{(Old)}\) * 100 = \(\frac{(1024x - x)}{x}\)* 100 = 1023 * 100 ----> 102300 %
Answer: D
03 Jun 2018, 14:21
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Using Exponent formulae and given data, we get constant k=2^1/3
So, after 30 days, k^30= 2^10= 1024.
Let initial population be y.
Then final population will be 1024y. And increase in population will be 1023y.
% increase= (1023y/y)*100= 102300%
Ans D
So, after 30 days, k^30= 2^10= 1024.
Let initial population be y.
Then final population will be 1024y. And increase in population will be 1023y.
% increase= (1023y/y)*100= 102300%
Ans D
