The population of a certain city was 146,000 in 2006, and the observed doubling time for the population is 18 years.

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(d) n(t) = 146,000 (2^(t/18))

500,000 = 146,000 (2^(t/18))

500,000/146,000 = 2^(t/18)

ln (500,000/146,000) = (t/18) ln 2

t = [ ln (500,000/146,000) ] / [ ln 2 ] x 18

= 32

This will occur during the year 2006 + 32 = 2038.

it actually 2037

That might be rounding issue. I kept all the numbers original and round it at the end.

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