Question

The population of a certain country 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, estimate the number of people initially living in the country.

Answer 1

To begin, we are told from the question that the rate of increase of the population of the country is proportional to the number of people presently living in the country. 

Let make N represent the population of the country at any given time t and N_o as the initial population. 

where k is the constant of proportionality.

For t=0, N = N_o

Therefore, 

                                             (1)

For t = 2 yrs, N = 2No

Substitute these values into (1)

k = 0.347

Therefore (1) becomes 

                     (2)

For t = 3 yrs, N = 20,000

Substitute these values into (2)

N_o = 7062

Therefore the number of people initially living in the country is 7062

 

Comments

Well explained.

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I love the way the question was answered. It's simple to understand.

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I agree with you