A half life is the amount of time it takes for half of a sample of an element to undergo radioactive decay.
For the first one, you know the half life is 3.8 days and you need to find out how much it will decay in 15.2 days. First, you need to figure out how many half lives the sample goes through. To do this, you divide 15.2 by 3.8 to get 4. Next, you divide the size of the sample in half four times. 4.38/2/2/2/2=0.27375g
For the second one, you can use logic. You can think of it like this: after one half life, you will have half of the sample. After two half lives you will have half of the remaining sample, or half of half of the sample, or 1/4 of the sample. So, knowing that you will have to wait two half lives to get a quarter of the substance, you multiply 5,700 by 2 to get 2,850 years.
Hope this helps!!
