Answer
After 30 hours, the activity of that sodium-24 sample is equal to 3.0 mCi.
Work Step by Step
1. Use the half life value for $^{24}_{11}Na$ as a conversion factor to calculate the amount of half-lives after 30 hours.
number of half lives = $30 h \times\frac{1 half-life}{15 h} = $ 2.0 half-lives.
2. After a half-life, one-half of the sodium-24 decays. Therefore, the activity after that time is equal to $\frac{1}{2}$ of the initial activity.
Initial $^{24}_{11}Na$ activity: 12 mCi.
After one half-life:
$12$ $mCi$ $\times \frac{1}{2} = 6.0$ $mCi$
3. The same will occur on the following half-lives, so, repeat the process:
After the second half-life:
$6.0$ $mCi$ $\times \frac{1}{2} = 3.0$ $mCi$