At 3:30pm there will be approximately 0.5868mg of fluorine.
The original amount (10.0 mg) is going to be halved every half-life. So, every 110 minutes, the amount is halved. After the first hour, 10mg --> 5mg. Second hour, 5mg --> 2.5mg. And so on.
We have to first figure out how many half-lives are within the time period. From 8:00am to 3:30pm is 7 hours, 30 minutes, or 7.5 hours. To calculate how many hours 110 minutes is, divide by 60 minutes (1 hour) -->
We can figure out the number of half-lives by dividing our total amount of time by the length of a single half-life.
Number of half lives =
Leftover amount: Original amount x
= 10.0mg x