Suppose Jill's biological family tree looks like the diagram at right. You can model recursively the number of people in each generation.
a. Make a table showing the number of Jill's ancestors in each of the past five generations. Use u0 to represent Jill's generation.
b. Look in your table at the sequence of the number of ancestors. Describe how to find un if you know un-1. Write a recursive formula.
c. Find the number of the term of this sequence that is closest to 1 billion. What is the real-world meaning of this answer?
d. If a new generation is born every 25 years, approximately when did Jill have 1 billion living ancestors in the same generation?
e. Your answer to 12c assumes there are no duplicates, that is, no common ancestors on Jill's mom's and Jill's dad's sides of the family. Look up Earth's population for the year you found in 12d. You will find helpful links at www.keymath.com/DAA. Write a few sentences describing any problems you notice with the assumption of no common ancestors.