Question

The half-life of carbon-14 is 5,730 years. How many grams of parent material will remain from a 120-gram sample of carbon-14 after 2 half-lives?
90

60

30

15

Answer 1

After one half-life . . . 1/2 of the total parent material

After another half-life . . . 1/2 of the half remains = 1/4 of the total original parent

If the original parent is 120 grams, then (1/4 x 20) = 30 grams remains
after 2 half-lives.  It makes no difference what the substance is, or
how long its half-life is.

Answer 2

$t_{\frac{1}{2}}=5730\\ N_0=120\ g\\ t=2t_{\frac{1}{2}}=2\cdot5730=11460\\ N(t)=?\\\\ N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{\frac{1}{2}}}}\\ N(11460)=120\cdot\left(\frac{1}{2}\right)^{\frac{11460}{5730}}\\ N(11460)=120\cdot\left(\frac{1}{2}\right)^2\\ N(11460)=120\cdot\frac{1}{4}\\ N(11460)=30\ g$