Question

If country 'A' had a total area of 1,000,000 square km only 10% was cultivated. In 2010,
country 'A' had 50,000,000 populations. 1/5 was women they constituted to birth. The
total death was 15,000. You can assumed that from 500,000 newly born babies, 90%
were survived their first year of life. If number of emigrants and immigrants were 10,000
and 5,000 respectively. The growth rate was 3%. Then Find: (1 pts each)
1) Crud Birth Rate
7) Number of Infant Death
2) General Fertility Rate
8) Infant Mortality Rate
3) Crud Death Rate
9) Doubling time
4) Rate of Natural increase
10) Crud Density
5) GR
11) Agricultural Density
6) No of Women
12) 12. Net Migration Rate

Help me with steps please.

Answer 1

1) Crude birth rate is the number of births per 1000 of population within a year:

$$CBR=\frac{500,000}{50,000,000}\cdot1000=10\text{ births/1000 people}.$$

7) Number of Infant Death is how many children died:

$$NID=(100-90)/100\cdot500,000=\\=50,000\text{ infant deaths}.$$

2) General Fertility Rate is how many children can be born by a woman on average:

$$GFR=\frac{500,000}{\frac{1}{5}\cdot50,000,000}=0.05,$$

or 5 births per 100 women.

8) Infant Mortality Rate is how many deaths per 1000 live births:

$$NID=\frac{100-90}{100}\cdot\frac{500,000}{50,000,000}\cdot1000=\\=1\text{ infant death/1000 people}.$$

3) Crud Death Rate is how many deaths in total per 1000 people:

$$CDR=\frac{15,000}{50,000,000}\cdot100000=\\=30\text{ deaths/100,000 people}.$$

9) Doubling time is the time it takes to double the population. We have 50,000,000 people. 3% add each year, which means that the next year the population will be

$$P_1=50,000,000\cdot(1+\frac{3}{100})=51,500,000,$$

the following year

$$P_2=51,500,000\cdot(1+\frac{3}{100})=53,045,000,$$

and

$$P_n=50,000,000\cdot1.03^n,$$

where n - the number of years. Hence:

$$50,000,000\cdot1.03^n=100,000,000,\\ 1.03^n=2,\\ n=\text{log}_{1.03}2=23.45\text{ years}.$$

4) Rate of Natural increase is the crude birth rate minus crude death rate:

$$RNI=CBR-CDR=10\cdot100-30=\\=970\text{ people/100,000 people a year}.$$

10) Crude Density is how many people per total area:

$$CD=\frac{50,000,000}{1,000,000}=50\text{ people/km}^2.$$

5) GR (growth rate) is how many percent the population each next year is higher than the previous, it is 3%.

11) Agricultural Density is how many km squared of cultivated lands there are per total area of the country:

$$AD=\frac{(10/100)\cdot1,000,000}{1,000,000}=\\=0.1\text{ km}^2\text{ cultivated per 1 km}^2 \text{ of land area}.$$

6) No of Women:

$$NoW=\frac{1}{5}\cdot50,000,000=10,000,000.$$

12) Net Migration Rate is the difference between how many entered and left the country per 1000 of population:

$$NMR=\frac{5000-10000}{1000}=-5\text{ migrants/1000 people}.$$