 A company's profits increase by 15% in the first year and 20% in the second year. What is 
the total percentage increase over the two years?

To calculate the total percentage increase over two years, we need to account for the fact that the increases are compounded year-over-year. Here's how we can do it:

### Step-by-Step Calculation:
1. Let the initial profit be \( P \).
2. In the first year, the profit increases by 15%, so the profit after the first year is:
   \[
   P \times (1 + 0.15) = P \times 1.15
   \]
3. In the second year, the profit increases by 20% on the new amount, so the profit after the second year is:
   \[
   P \times 1.15 \times (1 + 0.20) = P \times 1.15 \times 1.20 = P \times 1.38
   \]
4. The total profit after two years is \( P \times 1.38 \), meaning the profit has increased by 38% over the two years.

Thus, the total percentage increase over the two years is **38%**.

Would you like any further explanation or details?

Here are 5 related questions to consider:
1. How would the total increase change if the percentages were reversed (20% in the first year and 15% in the second)?
2. What would the percentage increase be if the company had a 10% decrease in the third year?
3. How do you calculate the percentage change if there are different changes across several years?
4. What if the company saw a 0% increase in the second year? How would the total increase be affected?
5. How can you express the relationship between compounded growth rates mathematically?

**Tip**: For multiple year percentage increases, always compound the growth rates instead of simply adding them together.

A company's profits increase by 15% in the first year and 20% in the second year. What is the total percentage increase over the two years?

Learn how to calculate the total percentage increase when a company's profits rise by 15% in the first year and 20% in the second year. The step-by-step solution covers compound growth concepts and the proper formula for calculating total increase. Suitable for Grades 9-12 students and anyone interested in financial mathematics.

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