Question

Given the following information, compute the missing columns in the life table:

Age (x)	Number Alive	bx	lx	sx	mx
0	452	0
1	322	2
2	111	3
3	64	1
4	25	1
5	0	0

After completing the table, compute the number of individuals in each age class for the next two generations.

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Answer 1

GIVEN:

X is the age of an individual measured in years.

represents the number of persons alive or the number of individuals surviving at the start of age interval x.

is the number born in the interval.

TO CALCULATE:

​ is the proportion (scaled from 0 to 1) of individuals surviving at the start of age interval x given by,

  

where ​ is the total number of persons.

​ is the age-specific survival given by,

is the mortality rate in year x = proportion of individuals of age x dying by age x+1.

  

Now let us fill in the missing values using these formulas.

Age (x)
0	452	0	1	322/452=0.71	0.29
1	322	2	0.71	111/322=0.34	0.66
2	111	3	0.25	64/111=0.58	0.42
3	64	1	0.14	25/64=0.39	0.61
4	25	1	0.06	0/25=0	1
5	0	0	0

To compute the number of individuals in each age class for the next two generations:

1	0	0
0.71	2	1.42
0.25	3	0.75
0.14	1	0.14
0.06	1	0.06
0	0	0

R₀ is the net replacement rate or the number of individuals in the next generation per individual in the current generation given by,

  

persons.

Thus a value of is greater than 1 which indicates a growing population. Since the value of ​ is 2, the number of individuals in each age class is more than double its size each generation.