Suppose that the population P(t) of a country satisfies the differential equation dP/dt = kP (600 - P) with k constant. Its population in 1960 was 300 million and was then growing at the rate of 1 million per year. Predict this country's population for the year 2030.

The country's population for the year 2030 is 368.8 million.

Step-by-step explanation:

The differential equation is:

Integrate the differential equation to determine the equation of P in terms of t as follows:

At t = 0 the value of P is 300 million.

Determine the value of constant C as follows:

It is provided that the population growth rate is 1 million per year.

Then for the year 1961, the population is: P (1) = 301

Then .

Determine k as follows:

For the year 2030, P (2030) = P (70).

Determine the value of P (70) as follows:

Thus, the country's population for the year 2030 is 368.8 million.

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