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.

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.

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.

Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half-lives can be found by using the expression 3^–t.

A. What fraction of substance remains after 7 half-lives?

B. After how many half-lives will the fraction be of the original?

One Fermi is equal to 10^–15 metre. The radius of a proton is 1.3 Fermis. Write the radius of a proton in metres in standard form.