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Find and solve a differential equation for the decay of a material with given properties

A given substance decays at a rate proportional to the square of the amount of the material present. At the end of one year there is 0.5 grams of the substance remaining.

  1. Create and solve a differential equation that governs the mass of the material present after t years.
  2. Find the decay constant of the material in units \operatorname{gm}^{-1} \operatorname{yr}^{-1}.

Incomplete.

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