Calcium-51 has a half-life of 4.5 days. only 0.75 gram remains of a sample that was initially 12 grams. how old is the sample of calcium-51?

How many times did the original sample lose 50% of its radioactivity ?

-- Start with. . . . . . . . . . . . 12 grams.
-- Lose half of it once. . . . . . 6 grams left.
-- Lose half of it again . . . . . 3 grams left.
-- Lose half of it again . . . . . 1.5 grams left.
-- Lose half of it again . . . . . 0.75 gram left.

-- How many times did it lose half ?    4 times.

-- How long does it take to lose half ?  4.5 days. 
                                                       (That's why it's called the 'half-life'.)

-- How long did it take to lose half, 4 times ?

                                           (4 x 4.5 days) = 18 days .