3.3+Predicting+Profit+0910

­­­ABP September 12, 2009 Math 7E **__ Variables And Patterns __** __ Big Idea __ Observation and description of changes in the world around us are the first steps in finding and learning about patterns. __ Essential Question __ How can I visually explain situations where one thing changes based on another?

3.3 – __Predicting Profit__ Based on the results of their survey, the tour operators decided to charge $350 per person for the tour. Of course, not all of this money would be profit. To estimate their profit, they had to consider the expenses involved in running the tour. Sidney estimated these expenses and calculated the expected profit for various numbers of customers. She made the graph below to present her predictions to her partners. Since the profit depends on the number of tour customers, she put the number of customers on the x-axis.

__ Notes __ : Pattern – A change that occurs in a predictable way. __ Journal Problem 3.3 __ A) **How** **much profit will be made if 10 customers go on the tour? 25 customers? 40 customers?**

- If 10 customers go on the tour, the profit will be $150. If 25 customers go on the tour, the profit will be $375, and if 40 customers go on the tour, the profit will be $600.

B) **How many customers are needed for the partners to earn a $200 profit? A $500 profit? A $600 profit?**

- 13-14 customers are needed for the partners to earn a $200 profit. 33-34 customers are needed for the partners to earn a $500 profit, and 40 customers are needed to earn a $600 profit.

C) **How does the profit change as the number of customers increases? How is this pattern shown in the graph?**

- The profit changes by increasing a certain amount as the number of customers increases. In the graph, this pattern is shown by the points rising in a line with equal distances between all the points.

D) **If the tour operators reduced their expenses but kept the price at $350, how would this change the graph?**

- If the tour operators reduced their expenses but kept the price at $350, then the graph’s points would rise in a steeper line than before, because the profit would be greater.

__ Journal Problem 3.3 Follow Up __ ** - **** If only one customer went on the tour, the profit would be $15. If 2 customers went on the tour, the profit would be $30. If 3 customers went on the tour, the profit would be $45, an if a 100 customers went on the tour, the profit would be $1500. The estimated profit for any number of customers would be $15 times the number of customers. **
 * In the profit graph, points at the intersection of two grid lines, such as (20, 300) and (40, 600) are easy to read. Use the "easy to read" points to figure out what the profit would be if only 1 customer went on the ** ** tour. How about 2 customers? 3 customers? 100 customers? Describe, in words, the estimated profit for any number of customers. **