Suppose the population of a city was 680,000 in 2015, it is growing at the rate of 12% per year. What is the population after 2015? In the year 2025?
*
1 point
1,200,000
2,100,000
2,168,238
2,500,000

To find the population of the city after 2015, given that it is growing at a rate of 12% per year, we can use the formula for exponential growth:

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

where:
- \( P(t) \) is the population after \( t \) years,
- \( P_0 = 680,000 \) is the initial population in 2015,
- \( r = 0.12 \) is the growth rate (12% per year),
- \( t \) is the number of years after 2015.

We need to find the population in the year 2025. The year 2025 is 10 years after 2015, so \( t = 10 \).

Substitute the values into the formula:

\[
P(10) = 680,000 \times (1 + 0.12)^{10}
\]

Let's calculate the value of \( P(10) \).The population of the city in the year 2025, after 10 years of growth at 12% per year, is approximately **2,111,977**.

Among the provided options, the closest choice is **2,100,000**.

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

### Additional Related Questions
1. What would the population be in the year 2030?
2. How long will it take for the population to double at the same growth rate?
3. What would be the annual growth rate if the population reaches 3 million by 2030?
4. How much would the population increase each year on average over the 10 years?
5. What would be the population if the growth rate were only 8% per year?

**Tip:** When dealing with exponential growth, always consider the effect of compounding over time.

Suppose the population of a city was 680,000 in 2015, it is growing at the rate of 12% per year. What is the population after 2015? In the year 2025?

Discover how to calculate the population of a city growing at a rate of 12% per year using the exponential growth formula. This example starts with a population of 680,000 in 2015 and estimates the population for the year 2025. Ideal for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation