Cerium-144 is a radioactive isotope with a half-life of 285 days. how long would it take for an initial sample of 15 grams of cerium-144 to decay until only 5 gram remains? a. about 452 days b. about 855 days c. about 570 days d. about 407 days

To solve this we are going to use the formula: 
where 
is the final amount aster a time 
is the initial amount 
is the time 
is the half-life

We know for our problem that , , and  , so lets replace those values in our formula:



Since  is the exponent, we are going to use logarithms to find its value:









We can conclude that the correct answer is: a. about 452 days.