The count of bacteria in a certain experiment was incresing at the rate of 2% per hour. Find the bacteria at the end of 2 hours if the count was initially 500000.

Answer

To solve the problem of finding the count of bacteria after 2 hours with an initial count of 500,000 and a growth rate of 2% per hour, we can use the formula for compound interest:

### Step-by-Step Solution:

1. **Identify the Variables**:
- Initial count (Principal, P) = 500,000
- Rate of increase (r) = 2% = 0.02 (as a decimal)
- Time (t) = 2 hours

2. **Use the Compound Interest Formula**:
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
Here, since the rate is already in decimal form, we can simplify it to:
\[ A = P \left(1 + r\right)^t \]

3. **Substitute the Values**:
Substitute the values into the formula:
\[ A = 500000 \left(1 + 0.02\right)^2 \]

4. **Calculate the Growth Factor**:
Calculate \(1 + 0.02\):
\[ 1 + 0.02 = 1.02 \]

5. **Raise to the Power of Time**:
Now raise \(1.02\) to the power of \(2\):
\[ (1.02)^2 = 1.0404 \]

6. **Calculate the Final Amount**:
Now multiply the initial count by the growth factor:
\[ A = 500000 \times 1.0404 = 520200 \]

7. **Final Result**:
Therefore, the count of bacteria at the end of 2 hours will be:
\[ A = 520200 \]

### Summary:
The count of bacteria after 2 hours is **520,200**.

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