So: 75 × (1.12)^3 = 75 × 1.404928 = 105.3696. - Groen Casting

Understanding the Context

This equation reflects exponential growth and helps us understand how steady percentage increases compound over time. Let’s unpack it step-by-step and explore its significance.

What Does 75 × (1.12)³ Represent?

At its core, this expression models growth scenarios where something increases by 12% each period. For instance:

Key Insights

• Finance: An investment of $75 that grows at 12% annually for three years.
  
• Population: A community growing at 12% per year over three years.
  
• Science and Industry: A microbial culture or chemical reaction multiplying by 12% each hour or day.

In each context, the growth compounds—meaning each period’s increase is calculated on the new, higher value—not just the original amount.

Breaking Down the Calculation

Let’s compute how the equation unfolds:

1. Base value: Start with 75
   
2. Growth factor: The annual increase is 12%, which as a decimal is 1.12
   
3. Time period: This growth applies over 3 periods (e.g., years)

Final Thoughts

Now plug into the formula:
75 × (1.12)³

First, calculate (1.12)³:
1.12 × 1.12 = 1.2544
Then, 1.2544 × 1.12 = 1.404928

Now multiply:
75 × 1.404928 = 105.3696

Why 105.3696?

The result, 105.3696, shows the total after three consecutive 12% increases. This demonstrates compounding effect—small, consistent growth accumulates significantly over time.

For example:

• After year 1: 75 × 1.12 = 84
  
• After year 2: 84 × 1.12 = 94.08
  
• After year 3: 94.08 × 1.12 = 105.3696