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.

An electron’s mass is approximately 9.1093826 × 10^–31 kilograms. What is this mass in grams?

At the end of the 20th century, the world population was approximately 6.1 × 10⁹ people. Express this population in usual form. How would you say this number in words?

About 230 billion litres of water flows through a river each day. How many litres of water flows through that river in a week? How many litres of water flows through the river in a year? Write your answer in standard notation.

A half-life is the amount of time that it takes for a radioactive substance to decay to one half of its original quantity. Suppose radioactive decay causes 300 grams of a substance to decrease to 300 × 2^–3 grams after 3 half-lives. Evaluate 300 × 2^–3 to determine how many grams of the substance are left.

Explain why the expression 300 × 2^–n can be used to find the amount of the substance that remains after n half-lives.