Question

Carbon-14 has a half-life of 5,730 years. After how many half-lives will 120 grams of Carbon-14 decay to 15 grams?

Answer 1

After 17190 years, Carbon-14 will reach a mass of 15 grams.

Pi is your initial amount (120 grams)
0.5 as your exponential base represents your HALF life hence 0.5
t represents the time elapsed
c represents your given half life value of (5730)
P(t) represents the exponential function of your half life

120/2 =60
60/2 = 30
30 /2 = 15

As you can see above, 3 half lives of 5730 years EACH degraded the carbon-14 to 15 grams. You divide each number by two as it is a HALF life.

P(t)= Pi (0.5) ^t/c
P(17190) = 120 (0.5) ^17190/5730
P(17190) = 120 (0.5) ^3
P(17190) = 15 grams

So your answers should be 3 half lives or after 17190 years have elapsed!