Hey there! Sign in to join this conversationNew here? Join for free

Data Errors Watch

Announcements
    • Thread Starter
    Offline

    2
    ReputationRep:
    The activity for a radioactive decay as a function of time is given by

    A=A_0e^{-\lambda t}

    At time t = 0, we measure A_0, and we also have an estimate of \lambda. At a later time t )assumed known without error) we estimate A from the formula.


    The question:

    1) Construct a formula for the error in A

    (I've done this)

    2)Give approximations for t small and t large. When does the transition between the two regimes occur? Interpret your results

    I don't know how to do the second part. Any ideas greatly appreciated.
    • Thread Starter
    Offline

    2
    ReputationRep:
    Nobody?
    • Study Helper
    Online

    13
    (Original post by Jagwar Ma)
    Nobody?
    I'm not familiar with the terms "t large" and "t small". Do you have definitions for them?

    It's possible someone may be able to assist knowing that extra information, even if I can't.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by ghostwalker)
    I'm not familiar with the terms "t large" and "t small". Do you have definitions for them?

    It's possible someone may be able to assist knowing that extra information, even if I can't.
    No idea. t small could be as t tends to -infinity, and t large could be as t tends towards + infinity?
    • Study Helper
    Online

    13
    (Original post by Jagwar Ma)
    No idea. t small could be as t tends to -infinity, and t large could be as t tends towards + infinity?
    OK, I can find nothing Googling either, so will assume it's not a technical term.

    What's your formula for the error from part 1)?

    I suspect they're looking for approximations for that formula for the different values of t.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by ghostwalker)
    OK, I can find nothing Googling either, so will assume it's not a technical term.

    What's your formula for the error from part 1)?

    I suspect they're looking for approximations for that formula for the different values of t.
    \frac{\sigma A^2}{A} = \frac{\sigma A_0}{A_0} +(-t \sigma \lambda)^2
    • Study Helper
    Online

    13
    (Original post by Jagwar Ma)
    ...
    Sorry, I can't help. It's a level of error analysis beyond my knowledge.

    :sad:
    • Study Helper
    Online

    13
    (Original post by Jagwar Ma)
    \frac{\sigma A^2}{A} = \frac{\sigma A_0}{A_0} +(-t \sigma \lambda)^2
    A further thought, as no one else has responded.

    For large t, your quadratic term will dominate, and we have

    \frac{\sigma A^2}{A} \approx ( \sigma \lambda)^2t^2

    And for small t, the quadratic term will tend to 0, as t tends to zero, so

    \frac{\sigma A^2}{A} \approx \frac{\sigma A_0}{A_0}

    Edit: Anyone more knowledgeable feel free to chip in (rep or PRSOM available ).
    Offline

    3
    ReputationRep:
    I agree.

    To begin with ("t small"), you errors will be dominated by the constant term. But as time goes on ("t large") they will be dominated by the quadratic term.

    For a transition point, you might reasonably choose the point where the two terms are equal (i.e. solve for t). Then look at whether your results were made before or after that, and hence what type of error is the dominant one.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    How are your GCSEs going so far?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.