Question

Radium decays according to the function Q(t) = Q0e-kt where Q represents the quantity remaining after t years and k is the decay constant 0.00043. What is the half-life of radium? Calculate how long it will take for 120g of radium to decay to 60g. Round your answer to the nearest year.

Answer 1

solve

hmmm
half life
well, 120 to 60 is half

60=120e^(-0.00043t)
solve for t
divide both sides by 120
1/2=e^(-0.00043t)
take ln of both sides
ln(1/2)=-0.00043t
divide both sides by -0.00043
ln(1/2)/-0.00043=t
t≈1611.97 years
about 1612 years