Question

According to the United Nations, in the year 2002, the population of the world was 6.1 billion people and was growing at an annual rate of about 1.5%. If this pattern were to continue, then every year, the population would be 1.015 times the population of the previous year. Thus, if P(t) is the world population (in billions) t years after the base year 2002.

(a) What was the population in 2004?
(b) What will the population be in 2010?

Answer 1

(a) 6.2843 billion

(b) 6.8716 billion

Explanation:

Since there is a constant growth rate of 1.5% per year, and the population in 2002 was 6.1 billion people. The general equation for the total world population, in billions, after 2002 is:

`P(t) = 6.1*(1+0.015)^t`

With t being the time, in years, after 2002.

a) What was the population in 2004?

`t=2004-2002=2\\P(2) = 6.1*(1.015)^2\\P(2) = 6.2843 \ billion`

b) What was the population in 2010?

`t=2010-2002=8\\P(8) = 6.1*(1.015)^8\\P(8) = 6.8716 \ billion`