Respuesta :
Answer:
b)-2.4% year
Explanation:
The population growth can be calculated by the following equation.
[tex]P(t) = P(0)e^{rt}[/tex]
In which [tex]P(t)[/tex] is the population in t years from now, [tex]P(0)[/tex] is the population in the current year and r(decimal) is the growth rate.[tex]e = 2.71[/tex] is the Euler number.
The current population of South Korea is 50 million, so [tex]P(0) = 50,000,000[/tex]
2750 is 2750 - 2019 is 731 years from now. So we have that [tex]t = 731[/tex]. The population is going to be extinct, so [tex]P(731) = 0[/tex].
So, we can replace the values of [tex]P(0)[/tex] and t in the equation, and see for which growth rate [tex]P(731) = 0[/tex].
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
[tex]r = -0.024[/tex]
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]P(731) = 50,000,000e^{-0.024*731} = 1.20[/tex]
Population of 1 person, basically extinct. This is the correct answer
c)-0.01% year'
[tex]r = -0.001[/tex]
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]P(731) = 50,000,000e^{-0.001*731} = 24,071,366[/tex]
Population still at 24 million, it does not goes extinct.
d)-0.012% year
[tex]r = -0.0012[/tex]
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]P(731) = 50,000,000e^{-0.0012*731} = 20,797,296[/tex]
Population still at almost 21 million, it does not goes extinct.
