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Math Help - re: solve exponential equations

  1. #1
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    Feb 2009
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    re: solve exponential equations

    Hi:
    This is not really so urgent, but I couldn't find anywhere that exponential questions seem to go. Any tips?

    Question is to solve the following:
    The current, i amps, flowing through an electrical circuit at time t seconds is known to be decreasing according to the equation
    i=Ie^(-5t)
    where I is the current initially flowing. Given that the initial current in this circuit is 2 amps, calculate how long it takes for the current to decrease to 0.5 amps, giving your answer in seconds correct to 2 d.p.

    hmmm!
    current is decreasing from 2 to 0.5. So, it has decreased by 1.5.
    Do I start here by - Ie^(-5t) becomes -5tIe - like in the basic logarithm rule
    loga^n = nloga

    If the initial current is 2, does this then become -5t2e?
    I think I'm lost already
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  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
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    Hello, morelemonzanybody?

    The current, i amps, flowing through an electrical circuit at time t seconds
    is known to be decreasing according to the equation . i \:=\:Ie^{-5t}
    where I is the current initially flowing.

    Given that the initial current in this circuit is 2 amps,
    calculate how long it takes for the current to decrease to 0.5 amps,
    giving your answer in seconds correct to 2 d.p.

    We are told the initial current is 2 amps.
    . . So the function is: . i \:=\:2e^{-5t}


    We are asked: When is  i = 0.5 ?

    We have: . 0.5 \:=\:2e^{-5t} \quad\Rightarrow\quad e^{5t} \:=\:4 \quad\Rightarrow\quad 5t \:=\:\ln 4


    Therefore: . t \;=\;\frac{\ln4}{5} \;\approx\;0.28 seconds.

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  3. #3
    Newbie
    Joined
    Feb 2009
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    re: thanks

    I like your algebra. It's much simpler/more concise than some methods I have seen.
    thank you.
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