I don’t understand how to get this problem.

Question

If 14 g of a radioactive substance are present initially and 8 yr later only 7 g​ remain, how much of the substance will be present after 9 ​yr?

Answer 1

Hello Tristin,

You can use the following equation to describe exponential decay:

A(t) = A_0 * (0.5)^(t/t_h) where A(t) is the final amount at time t, A_0 is the initial amount, t_h is the half-life (the time is takes for the initial amount to decrease by half), and t is the amount of time elapsed.

This sentence is key: "If 14 g of a radioactive substance are present initially and 8 yr later only 7 g​ remain" because 7g is HALF of 14g. That means the half-life is 8 years.

You now know everything else except A(t), which is what the problem wants you to find.

You know: A_0 = 14, t_h = 8, t = 9

So: A(t) = 14 * (0.5)^(9/8) = 14 * (0.5)^(1.125)

You would plug it in your calculator and it would get you a numerical value that will be the answer to "how much of the substance will be present after 9 ​yr?"

Cheers.