Q. 75.0( 1 Vote )

# The population of a city increases at a rate proportional to the number of inhabitants present at any time t. If the population of the city was 200000 in 1990 and 25000 in 2000, what will be the population in 2010?

Answer :

Let the initial population be P_{o} .

And the population after time t be P.

According to question,

⇒

⇒

⇒

Integrating both sides, we have

⇒ ∫ = k∫dt

⇒ log|P| = kt + logc……(1)

Given, we have P = 200000 when t = 1990

Putting the value in equation (1)

∴ log|200000| = k× 1990 + logc……(2)

we have P = 250000 when t = 2000

Putting the value in equation (1)

∴ log|250000| = k× 2000 + logc……(3)

On subtracting equation(2) from(3) we have,

log|250000| – log|200000| = k× (2000 – 1990)

⇒

⇒

⇒ ……(4)

Substituting the value of k from (4) in (2), we have

log|200000| = × 1990 + logc……(5)

Substituting the value of k, log c and t = 2010 in (2), we have

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