Question

1. 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. (12pts)

BR =

DR =

APGR =

DT =

Adjusted (True) Growth Rate =

Adjusted (True) Doubling Time =

Answer 1

1. Birth Rate: it is an average number of births in one year per thousand person in the population at mid year.

BR = (Total birth in a year/total population in mid year) X 1000

BR =  (50,000/1,000,000) x 1000 = 50

2. Death rate: It is an average number of death in one year per thousand person in the population at midyear, therefore

DR = (Total death/total population in midyear) X 1000

DR =   (10,000/1,000,000) x 1000 = 10

3. Annual Population Growth rate (APGR)

APGR = (Birth Rate - Death Rate)/ Death rate, therefore

APGR = (50 – 10) /10 = 4.0%

4. Doubling time is the total time required for a population to get double in size.

DT = ln(2)/ growth rate

70 / 4.0 = 17.5 years

Therefore, population will get double after 17.5 years

5. Adjusted (True) Growth Rate is equal to

= APGR + (NMR/death rate)

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

NMR = [(5000 - 20000)/100000]X1000 = -15

Therefore APGR will be

= 4.0 + (-15 / 10) = -6%

6. Adjusted (True) Doubling Time =

= ln (2)/ Adjusted growth rate

= 70 / -6 = - 11.66.

This negative sign indicating that it will never double in such condition