Question

10. The population of India is 1.353 billion, and expected to grow at the rate of one percent

annually for the forseeable future. Assuming population continues to grow at the same percent
rate, how long until the population reaches 2 billion people? Give your answer to the nearest
year. (4 minutes)

Answer 1

39 years

Explanation:

Adapt the formula A = P(1 + r)^n, letting P represent the original population, r the growth rate as a decimal fraction, and n the number of years.

Solve this for n:

2 billion = (1.353 billion)(1 + 0.01)^n

After simplification, we have:

2

--------- = 1.01^n

1.353

Taking the log of both sides, we get:

log 2 - log 1.353 = n log 1.01, or

log 2 - log 1.353 0.1697

------------------------ = -------------- = 39 years (rounded off from 39.28)

log 1.01 0.0043