A faster method could be to realize that doubling of population actually means raising the power by \(2\) hence if in 1852 the population was \(16000\) than in 1853 the population would be \(32000\)

Now we can do away with calculating the population for intermediaries between 1948 and 1953 because we know the lowest population will be that for the year 1848.

\(1953-1948 = 5\) hence population of \(1948 = \frac{32000}{2^5} = 1000\)

Therefore Range = \(32000-1000 = 31000\)

option E

_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes