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Printjmc
algebra intermediate
Problem
The function is graphed below. Each small box has width and height 1.
Larry writes the number 3 on his pinky finger. He then applies to 3 and writes the output on his ring finger. If Larry continues this process of applying and writing the output on a new finger, what number will Larry write on his tenth finger?
Larry writes the number 3 on his pinky finger. He then applies to 3 and writes the output on his ring finger. If Larry continues this process of applying and writing the output on a new finger, what number will Larry write on his tenth finger?
Solution
Reading from the graph we see that . Therefore Larry writes 6 on his second finger. Since we see that Larry writes 5 on this third finger. If we apply again, we see that Larry writes on the fourth finger. After this Larry writes on his fifth finger. Now the process repeats!
Since the first finger has 3 on it and the fifth finger also gets a 3 (4 turns later), the ninth finger will also get labeled as 3. Therefore Larry writes on his tenth finger.
Since the first finger has 3 on it and the fifth finger also gets a 3 (4 turns later), the ninth finger will also get labeled as 3. Therefore Larry writes on his tenth finger.
Final answer
6