Question

Out of a world population of approximately 6.6 billion, 1.2 billion people live in the richer countries of Europe, North America, Japan and Oceania and is growing at the rate of 0.25% per year, while the other 5.4 billion people live in the lees developed countries and is growing at the rate of 1.5%. What will be the world population in 5 years if we assume that these rates of increase will stay constant for the next 5 years. (round answer to 3 significant digits)

• A. 7.03 billion.
• B. 9.03 billion.
• C. 8.03 billion.
• D. 5.03 billion.

Answer 1

Answer: (A)

The correct option is A 7.03 billion.
$1.2$ billion live in rich countries and their growth rate is $0.25\%$ every year.

After one year :

$P_R=1.2+\frac{0.25}{100}\times 1.2$

$=1.2(1+\frac{0.25}{100})$

After $2$ years:

$P_R=1.2(1+\frac{0.255}{100})+\frac{0.25}{100}\left(1.2(1+\frac{0.25}{100})\right)$

$=1.2{(1+\frac{0.25}{100})}^2$

Continuing for $5$ years we get, $P_R=1.2{(1+\frac{0.25}{100})}^5$

Similarly for developing countries :

$P_L=5.4{(1+\frac{1.5}{100})}^5$

$\Rightarrow$ $P=P_R+P_L$

$=5.4{(1+\frac{1.5}{100})}^5+1.2{(1+\frac{0.25}{100})}^5$

$=7.03$ billion.