In 2000 the population of a district was 750,000. With a continuously compounding growth rate of approximately 4%, what will the population be in 2025?

Round the answer to the nearest whole number, and do not include the unit in your answer.

Provide your answer below

The population growth with continuous compounding follows the exponential growth formula:

\[
P(t) = P_0 \cdot e^{rt}
\]

Where:
- \(P(t)\) is the population at time \(t\),
- \(P_0\) is the initial population (750,000),
- \(r\) is the growth rate (4% or 0.04),
- \(t\) is the time in years (2025 - 2000 = 25 years),
- \(e\) is the base of the natural logarithm (approximately 2.71828).

We can now calculate the population in 2025:

\[
P(25) = 750,000 \cdot e^{0.04 \cdot 25}
\]

Let me compute this.The population of the district in 2025 will be approximately **2,038,711**.

Do you have any questions or would you like more details on this calculation?

Here are 5 related questions to further explore:

1. How would the result change if the growth rate was 5% instead of 4%?
2. What would the population have been in 2010 with the same growth rate?
3. How does continuous compounding differ from discrete annual compounding in population growth?
4. What is the formula to calculate the doubling time of the population with a continuous growth rate?
5. How does a growth rate affect the population over different time spans?

**Tip:** Always double-check growth rates and time intervals when solving exponential growth problems to avoid calculation errors.

In 2000 the population of a district was 750,000. With a continuously compounding growth rate of approximately 4%, what will the population be in 2025? Round the answer to the nearest whole number, and do not include the unit in your answer.

Learn how to calculate the population growth of a district from 750,000 in 2000 to an estimated 2,038,711 in 2025 using continuous compounding at a 4% growth rate. This problem demonstrates exponential growth concepts and uses the formula P(t) = P_0 * e^(rt). Suitable for Grades 10-12.

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