Example 3 Evaluating a Real-World Exponential Model

At the beginning of this section, we learned that the population of India was about 1.25 billion in the year 2013, with

an annual growth rate of about 1.2%. This situation is represented by the growth function P(t) = 1.25(1.012)t, where t

is the number of years since 2013. To the nearest thousandth, what will the population of India be in 2031?

Solution To estimate the population in 2031, we evaluate the models for t = 18, because 2031 is 18 years after 2013.

Rounding to the nearest thousandth,

P(18) = 1.25(1.012)18 1.549

There will be about 1.549 billion people in India in the year 2031.

The population of China was about 1.39 billion in the year 2013, with an annual growth rate of about 0.6%. This situation is represented by the growth function P(t)=(1.006)^t, where t is the number of years since 2013. To the nearest thousandth, what will the population of china be for the year 2031? How does this compare to the population prediction we made for india in Example 3?