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= 1023*100= 102300%

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