# The half-life of a radioactive material is the time required for an amount of this material to decay to one-half its original value. Show that for any radioactive material that decays according to the equation Q'=-rQ, the half-life t and the decay rate r satisfy the equation rt=ln 2.

Question

The half-life of a radioactive material is the time required for an amount of this material to decay to one-half its original value. Show that for any radioactive material that decays according to the equation Q'=-rQ, the half-life t and the decay rate r satisfy the equation rt=ln 2.