The population of a certain city was 146,000 in 2006, and the observed doubling time for the population is 16 years.

(d) Estimate when the population will reach 500,000.

Let y=ae^(kt), a=146000

Half life is 16 years, 292000=146000e^(16k), ln(2)=16k, k=0.043

So 500000=146000e^(0.043), ln500000-ln146000=0.043t, t=29

This will occur during the year 2006+29=2035.

Let me know how it goes, thanks.

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