### Home > A2C > Chapter 2 > Lesson 2.1.6 > Problem 2-87

Mr. C is such a mean teacher! The next time Mathias gets in trouble, Mr. C has designed a special detention for him. Mathias will have to go out into the hall and stand exactly 100 meters away from the exit door and pause for a minute. Then he is allowed to walk exactly halfway to the door and pause for another minute. Then he can again walk exactly half the remaining distance to the door and pause again, and so on. Mr. C says that when Mathias reaches the door he can leave, *unless* he breaks the rules and goes more than halfway, even by a tiny amount. When can Mathias leave? Prove your answer using multiple representations. 2-87 HW eTool (Desmos). Homework Help ✎

Remember to fill in the table.

Use the eTool below to view a graph and complete a table showing Mathias' progress towards the door over time.

Click the link at right for the full version of the eTool: A2C 2-87 HW eTool