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(Moderator's note: thread moved from "Differential Equations")

By natural increase, a city, whose population is 40,000, will double in 50 years. There is a net addition of 400 persons per year because of people leaving and moving into the city. Estimate its population in 10 years.

My book gives an answer of 50,240, but I am not sure how to get here. Usually I would put up the work I've already done, but it's all waaayyy off. I have, however, only tried to tackle it the "standard" simplest way, and haven't yet tried introducing a change of variables.

By natural increase, a city, whose population is 40,000, will double in 50 years. There is a net addition of 400 persons per year because of people leaving and moving into the city. Estimate its population in 10 years.

My book gives an answer of 50,240, but I am not sure how to get here. Usually I would put up the work I've already done, but it's all waaayyy off. I have, however, only tried to tackle it the "standard" simplest way, and haven't yet tried introducing a change of variables.

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