Answer
After 2.5 days, the activity of that sodium-24 sample is equal to $0.75$ $mCi$.
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 2.5 days. You will also need the conversion factor: $1$ $day = 24$ $h$.
number of half lives = $2.5 days \times \frac{24 h}{1day} \times \frac{1 half-life}{15h} = 4.0$ 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:
$6.0$ $mCi$ $\times \frac{1}{2} = 3.0$ $mCi$
After the third half-life:
$3.0$ $mCi$ $\times \frac{1}{2} = 1.5$ $mCi$
After the fourth half-life:
$1.5$ $mCi$ $\times \frac{1}{2} = 0.75$ $mCi$