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Math Help - Exponetial and Log case study

  1. #1
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    Exponetial and Log case study

    The number of observable facts that a witness to a motor vehicle accident can reliably recall can be modeled by the function R(t) = Ae^-kt , where A represents the number of observable facts a witness can recall immediately following an accident, t is the time in weeks after the accident, and k (where 0 < k <1) is an index related to the individual. For a particular witness to an accident, k =0.75, and A=140.

    1. Determine the number of facts that she should be able to recall after 2 weeks.

    31 facts, after 2 weeks

    Working:
    R(t) = Ae^-kt

    R(2) = 140e^-0.75*2

    140e^-1.5 = 31.238


    2. How long to the nearest half-day would it take according to this model for the witness to forget half the facts (i.e. find the ‘recall half-life’)?
    6.5 days

    Working:
    e^-0.75 = 0.5
    ln e^-0.75 = ln 0.5
    -0.75 = ln 0.5
    t = ln 0.5/-075 = 0.92419624

    0.92419624 * 7 (days in a week) = 6.5 (1 dp)


    3. Find a value of k for another witness that would give a ‘recall half life’ of 5 days (to 3dp). [Care with units, the unit for time t used in this model is weeks]

    k = 0.97

    Working:

    5 days, 5/7 = 0.714 weeks

    e^-k*0.714 = 0.5
    ln e^-k*0.714 = ln 0.5
    -k(0.714) = ln 0.5
    k = ln 0.5/-0.714 = 0.970179437

    I'm unsure of the last one, can anyone please have a look at these?

    Thanks
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  2. #2
    MHF Contributor
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    Hi

    According to me everything you have done is correct
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