https://file.aiquickdraw.com/mathbot/file/1729049781851vadi7fmv.jpg

The question shown in the image asks:

"A city has a population of 300,000 people. Suppose that each year the population grows by 4.25%. What will the population be after 10 years?"

### Step-by-Step Solution:
This problem involves **exponential growth**, where the population grows by a fixed percentage each year. The formula for exponential growth is:

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

where:
- \(P(t)\) is the population after \(t\) years,
- \(P_0 = 300,000\) is the initial population,
- \(r = 0.0425\) is the growth rate (4.25% expressed as a decimal),
- \(t = 10\) is the number of years.

### Substituting the values into the formula:

\[
P(10) = 300,000 \times (1 + 0.0425)^{10}
\]

\[
P(10) = 300,000 \times (1.0425)^{10}
\]

Using a calculator:

\[
1.0425^{10} \approx 1.5194
\]

\[
P(10) = 300,000 \times 1.5194 = 455,820
\]

### Final Answer:
The population after 10 years will be approximately:

\[
\boxed{455,820} \, \text{people}.
\]

Let me know if you'd like further clarification or details!

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**Follow-up Questions:**
1. How would the result change if the growth rate were 5% instead?
2. What is the population after 5 years with the same 4.25% growth rate?
3. How long will it take for the population to double at this growth rate?
4. What formula would apply if population growth were decreasing annually instead?
5. How does compound interest relate to this type of problem?

**Tip:** Remember to always convert percentages to decimals before calculations (e.g., 4.25% becomes 0.0425).

A city has a population of 300,000 people. Suppose that each year the population grows by 4.25%. What will the population be after 10 years?

Calculate the population growth for a city with an initial population of 300,000, experiencing a 4.25% annual growth rate. Detailed step-by-step solution using the exponential growth formula to find the population after 10 years.

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