A population of 2.5 million is growing exponentially.
a) What is the population 13 years later if the population has: continuous growth rate of 12%
 per year: 


To solve for the population after 13 years with an exponential growth rate, we can use the formula for continuous exponential growth:

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

Where:
- \( P(t) \) is the population after time \( t \) (in years),
- \( P_0 \) is the initial population,
- \( r \) is the continuous growth rate (expressed as a decimal),
- \( t \) is the time in years,
- \( e \) is Euler’s number, approximately 2.71828.

### Given values:
- Initial population \( P_0 = 2.5 \text{ million} \),
- Growth rate \( r = 12\% = 0.12 \) per year,
- Time \( t = 13 \) years.

Let's calculate the population after 13 years:

\[
P(13) = 2.5 \cdot e^{0.12 \cdot 13}
\]

I'll compute this next.The population after 13 years, with a continuous growth rate of 12% per year, will be approximately 11.9 million.

Would you like a detailed breakdown or explanation? Here are some related questions you might find helpful:

1. How does continuous growth differ from other types of growth models?
2. How would the population change if the growth rate were reduced to 8%?
3. What is Euler’s number, and why is it used in continuous growth calculations?
4. How would a logistic growth model affect the population projection over time?
5. What happens to the population if the growth rate remains constant for 50 years?

**Tip:** Exponential growth often models real-world phenomena where the growth rate is proportional to the current amount. In practice, factors like resources can limit this growth.

A population of 2.5 million is growing exponentially. What is the population 13 years later if the population has a continuous growth rate of 12% per year?

Explore how to calculate the future population of 2.5 million after 13 years with a continuous growth rate of 12% per year. Learn about the exponential growth formula and key concepts in population modeling. Suitable for students in Grades 10-12.

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