If India had a population of 1.05 billion in 2002 with a steady growth rate of .9%, when would its population reach 4.2 billion?
To find out when India's population would reach 4.2 billion, we can use the compound interest formula since the population is growing at a steady rate.
Let's break down the problem step by step:
1. Start with the given information:
- Initial population in 2002: 1.05 billion
- Growth rate: 0.9% (0.009 as a decimal)
2. The compound interest formula we can use is:
P = P0 * (1 + r)^t
where:
- P is the final population
- P0 is the initial population
- r is the growth rate
- t is the time in years
3. We need to solve for t, so rearrange the formula:
t = log(P/P0) / log(1 + r)
4. Now, substitute the given values into the formula:
P = 4.2 billion (desired population)
P0 = 1.05 billion (initial population)
r = 0.009 (growth rate)
5. Plug these values into the formula and calculate the result:
t = log(4.2/1.05) / log(1.009) ≈ 135.81
Therefore, India's population would reach approximately 4.2 billion in around 135.81 years from 2002.