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.

Question

Valentina Dean

Mathematics

26 September, 00:40

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.

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Fernando Doyle · 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).