While studying her family’s history. Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she has had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex.
A. Make a table and a graph showing the number of ancestors in each of the 12 generations.
B. Write an equation for the number of ancestors in a given generation n.
A. Table showing number of ancestors in each of the 12 generations:
Graph showing number of ancestors in each of the 12 generations:
B. Let the number of ancestors be ‘a’.
From the table, we know that
⇒ a = 20, 21, 22, 23, 24 … 210, 211, 212.
∴ a = 2n where n is the generation
is the equation for number of ancestors in a given generation n.