Question

Tritium, the heaviest form of hydrogen, is a critical element in a hydrogen bomb. It decays exponentially with a half-life of about 12.3 years. Any nation wishing to maintain a viable hydrogen bomb has to replenish its tritium supply roughly every 3 years, so world tritium supplies are closely watched. Construct an exponential function, Upper A left-parenthesis t right-parenthesis, that shows the remaining amount of tritium as a function of time as 100 grams of tritium decays (about the amount needed for an average size bomb) where Upper A is measured in grams and t is measured in years.
Round numbers to three decimal places, if required.

Answer 1

A(t)=100e^(-rt).
We need to find r. When t=12.3 A(t)=50 (half of 100) = 100e^(-12.3r).
ln(0.5)=-12.3r so r=ln(0.5)/-12.3=0.0564 approx. So A(t)=100e^(-0.0564t).