# Homework Assignment

This assignment involves user-defined functions and solving equations.

1. Derive and define a function that takes an interest rate R as its parameter and returns the number of years that it would take an investment at that rate to triple in value under continuous compounding.
2. Derive and define a function that takes an interest rate R as its parameter and returns the number of years it would take an investment to triple in value under annual compounding.
3. Derive and define a function that takes an interest rate R and an integer m, and returns the effective annual interest rate of an investment made at rate R that is compounded m times per year.
4. Define a function that takes as its argument an integer n and returns the number of feet by which a stack of n one-foot blocks will extend if they are stacked according to the plan developed in the last lesson.
5. In 1900 the estimated population of the world was 1.6 billion. In 1990 the estimated population was 5.236 billion. Assuming that the growth was at a constant rate, what has been the annual rate of population increase during that period? What will the world population be in 2040 if that rate holds?

Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah