July 16th 2024 Investigation Worksheet 1 Investigation 1 July 16th 2024 Investigation Worksheet 1 Investigation 2 Luis wants to join a gym. He finds one that charges a $100 membership fee to join and $5 every time he uses the facilities. What formula will help Luis to calculate how much he will pay in a given number of visits? If he goes to the gym 12 times in the first month, how much will he pay that month? Luis's friend Elijah decides to join a different gym. His has no membership fee but charges $15 per use. How many times does each of them need to use their gym before they have paid the same total amount? 1. Complete the table below of Luis's and Elijah's gym fees: 2. What patterns do you see emerging? 3. Which pattern is increasing faster? 4. When will the fees paid by Luis and Elijah be the same? 5. Are there any limitations to these patterns? Will they eventually reach a maximum value? July 16th 2024 Investigation Worksheet 1 6. Write down the first few terms for Luis. 7. Describe the pattern. 8. Justify the general expression (U r) for Luis at the bottom of the table below. 9. Write down the first few terms for Elijah. 10. Describe the pattern. 11. Complete the table below: 12. The general term for Luis can be simplified from u = 100+5(n-1) to u = 5n + 95. Justify this simplification. July 16th 2024 Investigation Worksheet 1
