Question

Consider the following information, which are estimates as of mid-2019.

Consider the following information, which are estimates as of mid-2019.

Country	Population Size	Birth Rate	Death Rate
United States	329.2 million	12	9
China	1388.0 million	11	7
Finland	5.5 million	9	10

For each country listed above, calculate r and how many people there will be in mid-2020 if population growth is exponential. Use the differential equation (dN/dt) for exponential population growth that was presented in Lecture.

Answer 1

r is the Net Productive rate which is given by Birth date - Death rate

Country	Birth Rate	Death Rate	Net Productive rate (r)
United States	12	9	3
China	11	7	4
FInland	9	10	-2

dN/dt = r * N

Here N is the Population size, r is the Net productive rate calculated in the above table

For United States

dN/dt = 3 * 329.3 million

= 987.9 million

since the time difference is only 1 year, dt will be 1

so N2020 - N2019 = 987.9

so N2020 = 987.9 + 329.3

= 1317.2 million

For China

dN/dt = 4 * 1388 million

= 5552 million

since the time difference is only 1 year, dt will be 1

so N2020 - N2019 = 5552

so N2020 = 5552 + 1317.2

= 6869.2 million

For Finland

dN/dt = (-1) * 5.5 million

= - 5.5 million

since the time difference is only 1 year, dt will be 1

so N2020 - N2019 = -5.5

so N2020 = -5.5+ 5.5

= 0

I am not sure whether the birth rate is per 1000 or per 100000 but the units are not given here so i have taken the birth rate and death rate as given in the table