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Population at time t will be calculated as per below formula

P(t) = P0(1+r)^t
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8000 x (growth factor)^9 = 64000
x^9 = 8 = 2^3
x = 9 underroot 2^3 = 2^1/3

Now, 2^1/3^y = 256000/8000 = 32, where y is the total time required
2^y/3 = 2^5
Hence y = 15 hours, Answer (E)
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From 10 AM to 7 PM is 9 hours.
The population grows from 8,000 to 64,000, which is a factor of 8 = 2^3

So, the population doubles every 3 hours.
To go from 64,000 to 256,000 is a factor of 4 = 2^2, which takes: 2×3=6 hours
Starting from 7 PM, 6 hours later is 1 AM (next day).
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