### Home > CAAC > Chapter 14 > Lesson 14.2.1.6 > 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 *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.

Make a visual representation of Mathias' punishment.

Label the classroom and his starting point.

Then label the second point. It should be

Keep dividing the distance in half until you reach a number less than

Mathias can never leave. If he reaches the door it will be because he broke a rule.

Try writing an exponential equation to represent this.