Question

Out of the 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 other $5.4$ billion people live in the less developed countries and is growing at the rate of $1.5\%$. What will be the world population in billions 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)

Answer 1

Given: $1.2$ 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:

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

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

Similarly for developing countries:

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

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

$=7.03$ billion

Hence, the correct answer is $7.03$ billion.