e. What happens to the cost per person if the number of people changes: - From 1 to 3 ? - From 2 to 6 ? - From 3 to 9 ?

To determine how the **cost per person** changes as the number of people increases, we'll assume that the **total cost remains constant**. Under this assumption, the cost per person decreases as the number of people increases because the same total cost is being shared among more individuals. Here's a breakdown of each scenario: 1. **From 1 to 3 People:** - **Initial Cost per Person:** If the total cost is \( C \), then for 1 person, the cost per person is \( C \). - **New Cost per Person:** When the number increases to 3, the cost per person becomes \( \frac{C}{3} \). - **Effect:** The cost per person **decreases to one-third** of the original amount. 2. **From 2 to 6 People:** - **Initial Cost per Person:** For 2 people, the cost per person is \( \frac{C}{2} \). - **New Cost per Person:** When the number increases to 6, the cost per person becomes \( \frac{C}{6} \). - **Effect:** The cost per person **decreases to one-third** of the original amount. 3. **From 3 to 9 People:** - **Initial Cost per Person:** For 3 people, the cost per person is \( \frac{C}{3} \). - **New Cost per Person:** When the number increases to 9, the cost per person becomes \( \frac{C}{9} \). - **Effect:** The cost per person **decreases to one-third** of the original amount. **Summary:** - **Increasing the number of people from 1 to 3, 2 to 6, or 3 to 9 all result in the cost per person decreasing to one-third** of the original cost per person. **Important Considerations:** - **Assumption of Constant Total Cost:** This analysis assumes that the total cost \( C \) does not change with the number of people. In real-world scenarios, factors like bulk discounts, varying resource usage, or differing service levels can affect the total cost. - **Variable Total Cost:** If the total cost changes with the number of people (e.g., \( C \) increases with more people due to additional resources needed), the cost per person might not follow the inverse relationship precisely. If there are additional factors or specific cost structures involved in your scenario, please provide more details for a more tailored analysis.