Question

The half-life of a radioactive substance is 5 minutes. how much of an original mass of 100 grams remains after half an hour?

Answer 1

\[31^{\exp}10\]

Answer 2

for 1/2 life problems, remember 1/2 (half-life should remind you of 1/2)
raised to the number of half-lives.

If the half-life is T, the number of half-lifes is how many T's have gone by.
you find this by dividing the time by T

for your problem T is minutes and 30 minutes went by. The number of half-lifes is 30/5 =6
so raise 1/2 to the 6th power

\[ \left(\frac{1}{2}\right)^{6} \]
you get
1/64
multiply this by how much you started with, 100 g
you get
\[ \frac{100}{64} = 1.5625 g\]