Question

South Korea (population 50 million) fears that its native population may be extinct by the year 2750. What is the best estimate of the population growth rate in South Korea? a) 0.012 % year' b)-2.4% year' c)-0.01% year' d)-0.012 year

Answer 1

b)-2.4% year

Step-by-step explanation:

The population growth can be calculated by the following equation.

`P(t) = P(0)e^(rt)`

In which
`P(t)` is the population in t years from now,
`P(0)` is the population in the current year and r(decimal) is the growth rate.
`e = 2.71` is the Euler number.

The current population of South Korea is 50 million, so
`P(0) = 50,000,000`

2750 is 2750 - 2019 is 731 years from now. So we have that
`t = 731`. The population is going to be extinct, so
`P(731) = 0`.

So, we can replace the values of
`P(0)` and t in the equation, and see for which growth rate
`P(731) = 0`.

a) 0.012 % year

This is a positive growth rate, which means that the population will not be going extinct. So this is not the alternative

b)-2.4% year

`r = -0.024`

`P(t) = P(0)e^(rt)`

`P(731) = 50,000,000e^(-0.024*731) = 1.20`

Population of 1 person, basically extinct. This is the correct answer

c)-0.01% year'

`r = -0.001`

`P(t) = P(0)e^(rt)`

`P(731) = 50,000,000e^(-0.001*731) = 24,071,366`

Population still at 24 million, it does not goes extinct.

d)-0.012% year

`r = -0.0012`

`P(t) = P(0)e^(rt)`

`P(731) = 50,000,000e^(-0.0012*731) = 20,797,296`

Population still at almost 21 million, it does not goes extinct.