https://file.aiquickdraw.com/mathbot/file/172593977440930g3lde2.jpg

To solve this problem, we need to use the formula for exponential growth, since the population grows by 5% each year. The formula is:

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

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

From the question:
- Initial population \(P_0 = 700,000\)
- Growth rate \(r = 5\% = 0.05\)
- Time \(t = 22\) years

Now we can calculate:

\[
P(22) = 700,000 \times (1 + 0.05)^{22}
\]

Let me calculate that.The population of the city in 22 years will be approximately **2,047,683**.

Do you want further details or explanations? 

Here are some related questions to expand on this topic:
1. What happens to the population if the growth rate changes to 3%?
2. How would the population be affected if the time period was extended to 30 years?
3. What is the formula for population decline if the city loses 2% of its population each year?
4. How would the calculation change if the population grew at a constant rate instead of exponentially?
5. Can you find how long it would take for the population to double at this growth rate?

**Tip:** Exponential growth can increase values rapidly over time, so even small changes in the growth rate can have significant long-term effects.

Suppose a city with population 700,000 has been growing at a rate of 5% per year. If this rate continues, find the population of this city in 22 years.

Learn how to calculate the population growth of a city with 700,000 residents, growing at a rate of 5% per year over 22 years using the exponential growth formula. This detailed step-by-step solution is ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation