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The problem describes a situation where a value (650) is increased by 45%, repeatedly, \( n \) times.

### Step-by-step breakdown:
1. **Initial Value**: Start with 650.
2. **Increase by 45%**: This means after one increase, the new value is 650 + 0.45(650) = \( 650(1 + 0.45) = 650(1.45) \).
3. **Repeating the process**: The value is increased by 45% again, which means multiplying by 1.45 again.
4. **Generalizing for \( n \) times**: After \( n \) increases of 45%, the value will be multiplied by 1.45 for each increase. So, the final result after \( n \) increases is:
   \[
   650 \times (1.45)^n
   \]

### Expression for the final result:
The final result after \( n \) increases is given by the expression:
\[
\boxed{650 \times (1.45)^n}
\]

Would you like more details or have any questions?

Here are some related questions:
1. What would the final result be after 5 increases?
2. How does the result change if the percentage increase is changed to 30%?
3. What is the final result when \( n = 0 \), meaning no increases are applied?
4. How would the formula change if instead of 45%, the value was increased by 100% each time?
5. How does this formula relate to exponential growth in general?

**Tip:** Exponential growth occurs when a quantity increases by the same percentage repeatedly. The formula reflects this through repeated multiplication.

650 is increased by 45%. The result is then increased by 45%, and so on. In total, the increase is applied n times. Write an expression to represent the final result of this process.

Explore how to represent the final value after repeatedly increasing 650 by 45%. Learn the exponential growth process where the increase is applied n times, and the final result is modeled using the expression 650 × (1.45)^n. Suitable for high school students in Grades 9-12.

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