During the spring and summer of 1993, the Mississippi River flowed over its banks at many places from Minneapolis, Minnesota, to St. Louis, Missouri. After the first flood, eighth graders in Jefferson County offered to help bag sand for levees when the next threat came. The students organized a telephone tree to spread word of where and when the students should meet in an emergency. The principal would call four student-government officers; they would each call four other students, who would call four other students, and so on. Draw a diagram showing the first three levels of the telephone tree. Do not count the principal as one of the levels.
How many levels of the tree would be needed to reach all 4092 eighth graders in Jefferson Country?
What algebraic rule could be used to find the number of new calls at each level of the telephone tree?
(Source: Adapted from Mathematics Teaching in the Middle School, Nov-Dec 1995)