Question

A certain isotope decays so that the amount A remaining after t years is given by: A = A0 · e -0.03t where A0 is the original amount of the isotope. To the nearest year, the half-life of the isotope (the amount of time it takes to decay to half the original amount) is a0years.

Answer 1

a/2=ae^(-0.03t)

0.5=e^(-0.03t)  take the natural log of both sides

ln(0.5)=-0.03t

t=ln(0.5)/(-0.03)

t≈23 years (to the nearest whole year)