d. What hoppens to the cost per perion if the number of people doubles: . From 2 to 4 ? - From 5 to 10 ? . From 6 to 12 ? 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 ? fescribe any patterns you may have noticed.

To analyze how the **cost per person** changes as the **number of people** increases, we'll assume that the **total cost remains constant**. This means the cost is **evenly distributed** among all individuals involved. Here's a breakdown of each scenario: --- ### **d. What happens to the cost per person if the number of people doubles:** 1. **From 2 to 4 people:** - **Initial Cost per Person:** Total Cost / 2 - **After Doubling:** Total Cost / 4 - **Effect:** **Halved** (The cost per person decreases by 50%) 2. **From 5 to 10 people:** - **Initial Cost per Person:** Total Cost / 5 - **After Doubling:** Total Cost / 10 - **Effect:** **Halved** (The cost per person decreases by 50%) 3. **From 6 to 12 people:** - **Initial Cost per Person:** Total Cost / 6 - **After Doubling:** Total Cost / 12 - **Effect:** **Halved** (The cost per person decreases by 50%) --- ### **e. What happens to the cost per person if the number of people changes:** 1. **From 1 to 3 people:** - **Initial Cost per Person:** Total Cost / 1 = Total Cost - **After Increasing:** Total Cost / 3 - **Effect:** **Reduced to one-third** (The cost per person decreases by approximately 66.7%) 2. **From 2 to 6 people:** - **Initial Cost per Person:** Total Cost / 2 - **After Increasing:** Total Cost / 6 - **Effect:** **Reduced to one-third** (The cost per person decreases by approximately 66.7%) 3. **From 3 to 9 people:** - **Initial Cost per Person:** Total Cost / 3 - **After Increasing:** Total Cost / 9 - **Effect:** **Reduced to one-third** (The cost per person decreases by approximately 66.7%) --- ### **Patterns Observed:** 1. **Inverse Relationship:** There's an **inverse relationship** between the number of people and the cost per person. As the number of people **increases**, the cost per person **decreases**, provided the total cost remains unchanged. 2. **Proportional Decrease:** - **Doubling the Number of People:** Halves the cost per person. - **Tripling the Number of People:** Reduces the cost per person to one-third. 3. **Consistency Across Scenarios:** Whether doubling or tripling the number of people, the cost per person consistently decreases by the same proportional factor respective to the increase in the number of people. --- **Visualization Example:** | Number of People | Total Cost | Cost per Person | |------------------|------------|------------------| | 2 | \$100 | \$50 | | 4 | \$100 | \$25 | | 5 | \$100 | \$20 | | 10 | \$100 | \$10 | | 6 | \$100 | \$16.67 | | 12 | \$100 | \$8.33 | | 1 | \$100 | \$100 | | 3 | \$100 | \$33.33 | | 9 | \$100 | \$11.11 | This table illustrates how increasing the number of people reduces the cost each individual needs to bear. --- **Conclusion:** Increasing the number of people sharing a fixed total cost leads to a proportional decrease in the cost per person. Specifically, **doubling** the number of people **halves** the cost per person, while **tripling** the number of people reduces the cost per person to **one-third**. This inverse relationship ensures that costs become more manageable for each individual as more participants share the expenses.