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Math Help - Probability Question Relatiing to Blood Alcohol Level...PLEASE HELP!

  1. #1
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    Probability Question Relatiing to Blood Alcohol Level...PLEASE HELP!

    hello, I have this math question that i am stuck on..it relates to the blood alcohol level..there is 3 parts to this question.

    -The probality (in percent) P of having an automoible accident is related to the blood alcohol content of the driver t by the following function P(t) = e 21.459t

    1-The "legal" BAC level in Ohio is .08. If someone was driving at that level, what is the probaliity (in percent) that he or she will be in an accient?

    2-At what blood alcohol level would one have to be at in order to have a 50% chance of an accident?

    3-At what blood alcohol level would one have to be at in order to have a 75% chance of an accident?
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  2. #2
    Senior Member topher0805's Avatar
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    I am assuming that this is your equation:

    P(t) = e^{21.459t}

    Is this correct?
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  3. #3
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    Yes, that is correct
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  4. #4
    Senior Member topher0805's Avatar
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    1) Simply plug in 0.08 into your equation to get your answer:

    <br />
P(0.08) = e^{21.459\cdot 0.08}

    2) Set the expression equal to 50 and solve for t:

    50 = e^{21.459\cdot t}

    Take the natural log of both sides:

    ln 50 = ln e^{21.459\cdot t}

    Using laws of exponents:

    ln 50 = 21.459\cdot t

    Divide both sides by 21.459:

    t = \frac {ln 50}{21.459}

    3) Same as question 2, just with different numbers.
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