Example 3 from Algebra and Trigonometry, 6.1 Exponential Functions

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 $2031?$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

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,
$P (18) = 1.25 {(1.012)}^{18} \approx 1.549$

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

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

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 $P (t) = 1.39 {(1.006)}^{t},$ 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?

How did it go?

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solution

Your turn

Solution

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