Question

In a science experiment, a chemical solution is diluted by 13 every hour. If the initial concentration was 64 parts
per million (ppm), what will be the concentration after 4 hours? Show your work

Answer 1

To determine the concentration of the chemical solution after 4 hours of dilution by a factor of 13 every hour, we can follow these steps:

1. **Identify the initial concentration**: The initial concentration is given as 64 parts per million (ppm).

2. **Determine the dilution factor**: The solution is diluted by a factor of 13 every hour. This means that each hour, the concentration is reduced to \(\frac{1}{13}\) of its concentration from the previous hour.

3. **Calculate the concentration after each hour**:
- After 1 hour:
\[
\text{Concentration} = \frac{64}{13^1} = \frac{64}{13} \approx 4.923 \text{ ppm}
\]
- After 2 hours:
\[
\text{Concentration} = \frac{64}{13^2} = \frac{64}{169} \approx 0.378 \text{ ppm}
\]
- After 3 hours:
\[
\text{Concentration} = \frac{64}{13^3} = \frac{64}{2197} \approx 0.0291 \text{ ppm}
\]
- After 4 hours:
\[
\text{Concentration} = \frac{64}{13^4} = \frac{64}{28561} \approx 0.00224 \text{ ppm}
\]

4. **Final concentration after 4 hours**:
- The concentration after 4 hours is approximately \(0.00224 \text{ ppm}\).

Thus, the concentration of the chemical solution after 4 hours of dilution is approximately \(0.00224 \text{ ppm}\).