a sample pf a special atomic element decayed exponentially to 33% of its original mass after 8 days

Question

a) find the half life

b) find the percentage of the original mass remaining after 12 days

thanks so much!

Answer 1

0.33 = e^8k

ln 0.33 = 8k

-1.10866 ≈ 8k

-0.138582828 ≈ k

0.5 ≈ e^{-0.138582828 t}

ln 0.5 = -0.138582828 t

-0.693214718 ≈ -0.138582828 t

5.00168 ≈ t

Use k in exponential or t in half life formula to determine amount after 12 days.