In 2017, the populations of China and India were approximately 1.379 and 1.282 billion people,120 respectively. However, the annual population growth rate of
China was 0.41% while the population of India was
growing by 1.17% each year. If these growth rates remain constant, when will the population of India exceed
that of China?

We are tasked with determining when the population of India will exceed that of China given the following information from 2017:

- China's population: 1.379 billion
- India's population: 1.282 billion
- China's growth rate: 0.41% annually
- India's growth rate: 1.17% annually

We can model the populations of China and India as functions of time \( t \), where \( t \) is the number of years after 2017. The population growth is exponential, and we use the following formula for each country:

\[
P(t) = P_0 \times (1 + r)^t
\]
Where:
- \( P(t) \) is the population after \( t \) years,
- \( P_0 \) is the initial population (in 2017),
- \( r \) is the growth rate,
- \( t \) is the number of years.

### Population of China
\[
P_{\text{China}}(t) = 1.379 \times (1 + 0.0041)^t
\]

### Population of India
\[
P_{\text{India}}(t) = 1.282 \times (1 + 0.0117)^t
\]

We need to find \( t \) when India's population exceeds China's population:

\[
1.282 \times (1 + 0.0117)^t > 1.379 \times (1 + 0.0041)^t
\]

To solve this inequality, we can divide both sides by their respective constants and solve for \( t \). Let's calculate it.

The population of India will exceed that of China in approximately 9.67 years after 2017. This means India's population is projected to surpass China's population around the year **2026** if the growth rates remain constant.

Would you like further details on the calculations or have any other questions?

Here are 5 related questions to explore further:

1. How does exponential growth affect long-term population projections?
2. How would the result change if China's growth rate decreased?
3. What is the significance of a country's population growth rate for its economy?
4. How do population growth trends influence global resource distribution?
5. What could happen if India’s growth rate slows down in the coming years?

**Tip:** Exponential growth models can greatly magnify small differences in growth rates over long periods, leading to substantial differences in population sizes.

In 2017, the populations of China and India were approximately 1.379 and 1.282 billion people, respectively. However, the annual population growth rate of China was 0.41% while the population of India was growing by 1.17% each year. If these growth rates remain constant, when will the population of India exceed that of China?

Discover when India's population is projected to exceed China's using exponential growth rates from 2017. Learn how to model population growth with functions and solve inequalities using logarithms. Suitable for Grades 10-12 students.

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