The population of a certain is known to increase at a rate proportional to the number of people presently living in the country. If after two years the population has doubled, and after three years the population is 20,000 estimates the number of people initially living in the country.

Explanation

To solve the problem of estimating the initial population of a country where the population increases at a rate proportional to the current population, we can follow these steps:

### Step 1: Set up the differential equation
The rate of change of the population \( N \) with respect to time \( t \) is given by:
\[ \frac{dN}{dt} = kN \]
where \( k \) is a constant of proportionality.
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