# 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.

Step 1

Solving the differetial equation: Q'=-rQ

Step 2

Let the value of Q(t) at time t=0 be Q(0).

Then at time...

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