The population of a country was 251 million in 1980 and the continuous exponential growth rate was estimated at 2.6% per year. Assuming that the population of the country continues to follow an exponential growth model, find the projected population in 1997. Round your answer to 1 decimal place.
The approximate population in 1997 is 
 million people

To solve this problem, we'll use the formula for exponential growth:

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

Where:
- \(P(t)\) is the population at time \(t\).
- \(P_0\) is the initial population (251 million in 1980).
- \(r\) is the continuous growth rate (2.6% or 0.026 per year).
- \(t\) is the time in years from the initial population year (from 1980 to 1997, \(t = 1997 - 1980 = 17\)).
- \(e\) is the base of the natural logarithm, approximately 2.718.

Substitute the values into the formula:

\[
P(17) = 251 \cdot e^{0.026 \cdot 17}
\]

Let's calculate that now.The projected population of the country in 1997 is approximately 390.5 million people.

Would you like more details on the calculation or have any further questions?

Here are some related questions:
1. What would the population be in the year 2020 using the same growth rate?
2. How does continuous exponential growth differ from other types of population growth models?
3. How would a change in the growth rate affect the projected population?
4. What happens to the population size in the long run with exponential growth?
5. Can you apply this model to other variables, such as financial investments?

**Tip:** In continuous growth models, small changes in the rate can lead to large differences over long periods due to the compounding effect.

The population of a country was 251 million in 1980 and the continuous exponential growth rate was estimated at 2.6% per year. Assuming that the population of the country continues to follow an exponential growth model, find the projected population in 1997. Round your answer to 1 decimal place.

Learn how to calculate the projected population of a country using the continuous exponential growth model. With an initial population of 251 million in 1980 and a growth rate of 2.6% per year, find the estimated population in 1997. Includes step-by-step calculations and explanations. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation