A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

A radio active isotope decays according to the exponential decay equation where t is in days. Round to the thousandths place. For the half life: The half life is the solution (t) of the equation : a/2=ae^−4.457t

  • This Question is Closed
  1. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[A = A _{0}*e^{r*t}\] you want A to be half the original amount A sub zero. that is the equation they gave you

  2. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    notice now, both sides have an a, divide both sides by a to eliminate that

  3. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{ 1 }{ 2 }=e^{-4.457*t}\]

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now you do loge^1/2=-4.457?

  5. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    log base e is the natural log, ln you can do that to both sides

  6. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\ln(\frac{ 1 }{ 2 })=\ln(e^{-4.457*t})\]

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    0.6931=-1.4944?

  8. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm, do you remember the log exponent rule.. \[\log_{b}(x^a) = a *\log_{b} (x) \]

  9. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and also, \[\log_{b}(b) = 1 \]

  10. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so on the right, pull down the exponent into the front of the log... and replace the natural log of e with 1.

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im not good at this at all :(

  12. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\ln(\frac{ 1 }{ 2 })=\ln(e^{-4.457*t}) = -4.457t * \ln(e)\]

  13. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    just have to remember the rules for logs

  14. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ln(e) = 1, so ln(1/2) = -4.457*t just have to solve for t, with a calculator

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1.5550?

  16. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yep, just round to the thousandths place, 1.555 days

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Could you help me with one more please?

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    e^x+1=1.038?

  19. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is e^(x+1) all exponent, or just x

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    x+1

  21. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    similar to last prob.. take the ln of both sides ln[e^(x+1)] = ln(1.038)

  22. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    exponent rule brings (x+1) to the front (x+1) * ln(e) = ln(1.038)

  23. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    natural log of e is 1, so x + 1 = ln(1.038) x = ln(1.038) + 1

  24. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1.0372?

  25. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yep

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then rounded to the nearest thousandth it would just be 1.037?

  27. DanJS
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  28. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you!!!

  29. 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.