The total number of industries in a particular portion of the country is approximately 1,600. if the government has decided to increases the number of industries in the area by 20% year. Find the approximate number of industries after 2 years.

Answer

To find the approximate number of industries after 2 years with a 20% annual increase, we can use the formula for compound interest:

\[ A = P \left(1 + \frac{R}{100}\right)^T \]

where:
- \( A \) = the amount after time \( T \)
- \( P \) = the principal amount (initial number of industries)
- \( R \) = the rate of increase (percentage)
- \( T \) = time in years

### Step-by-Step Solution:

1. **Identify the initial values:**
- Initial number of industries, \( P = 1600 \)
- Rate of increase, \( R = 20\% \)
- Time period, \( T = 2 \) years

2. **Convert the percentage rate into a decimal:**
- \( R = 20\% = \frac{20}{100} = 0.20 \)

3. **Substitute the values into the formula:**
\[ A = 1600 \left(1 + 0.20\right)^2 \]

4. **Calculate \( 1 + 0.20 \):**
\[ 1 + 0.20 = 1.20 \]

5. **Raise \( 1.20 \) to the power of 2:**
\[ (1.20)^2 = 1.44 \]

6. **Multiply by the initial number of industries:**
\[ A = 1600 \times 1.44 \]

7. **Perform the multiplication:**
\[ A = 2304 \]

### Conclusion:
The approximate number of industries after 2 years will be **2304**.

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