Question

Consider the following hypothetical population and compute the statistical measures below: #births = 50,000; #deaths = 10,000; #immigrants = 5,000; #emigrants = 20,000; mid-year population = 1,000,000. Show formulas and all relevant work.

BR =
DR =
APGR =
DT =
Adjusted (True) Growth Rate =
Adjusted (True) Doubling Time =

Answer 1

The birth rate refers to an average number of births in one year per thousand individuals in the population at mid-year.

BR = (total birth in an annum / total population in mid year) * 1000

BR = (50000 / 1000000) * 1000 = 50

Death rate refers to an average number of death in an annum per thousand individuals in a population at mid year. Thus,

DR = (total death / total population in mid year) * 1000

DR = (10000 / 1000000) * 1000 = 10

Annual population growth rate or APGR is calculated as:

APGR = (Birth rate - Death rate) / Death rate

APGR = (50 - 10) / 10 = 4.0 %

Doubling time is the whole sum time needed for a population to get double in size. It is calculated as DT = ln (2) / growth rate

70 / 4.0 = 17.5 years

Thus, population will get double in 17.5 years.

Adjusted (true) growth rate is equal to APGR + (NMR / Death rate)

And NMR = [(immigrants -emigrants) / total population] * 1000

NMR = [(5000 - 20000) / 1000000] * 1000 = -15

Thus, Adjusted (True) growth rate = 4.0 + (-15 /10) = -6%

The adjusted (true) doubling time = ln (2) / Adjusted growth rate

= 70 / -6 = -11.66

This negative sign shows that it will never get double in such situation.