Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

knbarwrgwddsg

  • 2 years ago

The half-life of radium is 1600 years. If the initial amount is q0 milligrams, then the quantity q(t) remaining after t years is given by q(t) = q02kt. Find k.

  • This Question is Open
  1. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So the equation is\[ q(t) = q_02^{kt} \]

  2. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Now, the quantity is going to be halved each time so we know \(k\) is going to be negative. \[ q(t)=q_0\left(\frac{1}{2}\right)^{-kt} \]

  3. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    We also know: \[ q(1600) = \frac{q_0}{2} = q\left(\frac{1}{2}\right)^{1} \]Since it is the half-life as well as\[ q(1600)=q_0\left(\frac{1}{2}\right)^{-k(1600)}\]See the pattern?\[ 1=-k(1600) \]

  4. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Solving for \(k\) gives us: \[ k = -\frac{1}{1600} \]

  5. wio
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @knbarwrgwddsg get it?

  6. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.