The halflife of a certain substance is 21 years How long wil

The half-life of a certain substance is 21 years. How long will it take for a sample of this substance to decay to 87 % of its original amount? Use the exponential decay model, A = A_0 e^kt, to solve, years (Round to one decimal place as needed.)

Solution

k = 0.693/haf life
= 0.693/21
= 0.033 year-1

A = Ao * e^(-k*t)
A / Ao = e^(-k*t)
0.87 = e^(-k*t)
ln (0.87) = -k*t
ln (0.87) = -0.033*t
t = 4.22 years
Answer: 4.22 years