A city has a population of 400,000 people. Suppose that each year the population grows by 3%. What will the population be after 12 years?

To find the population after 12 years given a 3% annual growth rate, we can use the formula for compound interest:

\[
P(t) = P_0 \times (1 + r)^t
\]

Where:
- \( P(t) \) is the population after \( t \) years.
- \( P_0 \) is the initial population.
- \( r \) is the growth rate per period (in decimal form).
- \( t \) is the number of years.

Given:
- \( P_0 = 400,000 \)
- \( r = 0.03 \) (3% growth rate)
- \( t = 12 \) years

Plugging in the values:

\[
P(12) = 400,000 \times (1 + 0.03)^{12}
\]

\[
P(12) = 400,000 \times (1.03)^{12}
\]

Now, let's calculate this:

\[
P(12) \approx 400,000 \times 1.42576 \approx 570,304
\]

So, the population after 12 years will be approximately **570,304** people.

Would you like more details or have any questions?

---

Here are 5 related questions:

1. How would the population change if the growth rate were 5% instead of 3%?
2. What would be the population after 20 years with the same 3% growth rate?
3. How can we adjust the formula if the population were to decrease by 2% annually?
4. What is the population doubling time given a 3% growth rate?
5. How does the compound interest formula apply to financial investments?

**Tip:** When dealing with exponential growth, small changes in the rate can lead to significant differences over time.

Explore how to calculate population growth using exponential growth and compound interest formulas. Given an initial population of 400,000 and an annual growth rate of 3%, find the population after 12 years. Learn the step-by-step solution with key mathematical concepts. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation