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# A country has a carrying capacity of 1,000,000 people?

A country has a carrying capacity of 1,000,000 people. It is said that the doubling time for

the population is 91.65 yr and the growth rate has been constant at 0.016 yr-1

.

a. The year is 2000, what is the initial population for this country?

b. To increase stability, the country decided to adopt a closed border policy for 50 years, but

at the end of this 50 year period the government will allow immigration at a rate of 5/100

people and an emigration rate 10x lower than the immigration rate. What will the

population of the country be at the end of the 50 year period if the population growth rate

and the carrying capacity remain constant and immigration and emigration are only

applied at the end of the 50-yr period?

c. Describe in words how growth rate dP/dt changes from when P is very small compared

to K or when P is similar to K.

### 3 Answers

- ZirpLv 75 months ago
this question does not make sense. Some countries have far more inhabitants than their carrying capacity

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- John PLv 75 months ago
The notion of a "carrying capacity" for a country (mythical or real) feels rather ridiculous. Australia has a population of 25 million in 3 million square miles. Japan has 127 million in 145,000 square miles, a far greater population density.

Who sets you strange questions of that sort? What sort of maths or geography are you studying?

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- 5 months ago
Does the question provide a current population count?

EDIT: I assume the question refers to 1M people in the year 2000.

Interest equation is P = F / (1 + i) ^ n

P = 1M / (1 + 0.016) ^ 91.65

P = 233449 people

EDIT 2: Was working this as an interest problem when it is completely different. Apparently the Logistic Equation is needed.

dP/dt = k * P (1 - P/K)

P = population at time t, k is a proportionality constant, and K is the carrying capacity

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- JD5 months agoReport
The population should increase at decreasing rate as it reaches the carrying capacity. This is just a guess though.

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