menu
bartleby
search
close search
Hit Return to see all results

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.

check_circleAnswer
Step 1

Solving the differetial equation: Q'=-rQ

fullscreen
Step 2

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

Then at time...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Calculus

Sorry about that. What wasn’t helpful?