I solved this question and I keep getting the answer 900% (A). The book states that the answer is 102,300%(D) and I am not understanding why. I looked at their explanation and wondered why are they writing it as a power of 2?
On first day, It was 1 cockroach
On 30th day, It will be 1024 cockroaches
So, 1 * ( 1 + x ) = 1024
x = (1024-1)/1 = 1023 or 102300%
How are you getting 1024?
The cockroach population doubles every 3 days so for a total of 30 days, It’ll be 2^10
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
population increase = ((new-old)/(old))*100 = ((1024x-x)/(x))100= 1023100= 102300%
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