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Thread: exponential decay

  1. #1 exponential decay 
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    I'm really stumped by this homework problem.

    N(t) = No (1-e^(-0.0372t))

    Where N(t) is final concentration at time t. No is final concentration.

    How long does it take to get 85% of final concentration.

    I can't figure out how to find the answer.

    First I was thinking that N(t)= 85 and No=100, since I'm guessing it starts at 100% concentration.

    85=100(1-e^(-0.0372t)) divide by 100

    85/100=(1-e^-0.0372t)) take ln of both sides

    ln(85/100) = 1-(-0.0372t) solve for t

    t= (ln(85/100))/(1-(-0.0372)) = -0.156690593 which must be wrong, since its coming out negative

    Then I though, maybe this is the right way to set it up.

    N(t)= 85 (1-e^-0.0372t))

    But then I have 2 variables, N(t) and t, when I really need to be solving for t.

    I can't figure out what I'm supposed to use for N(t) and No values.

    Unfortunately, there's no video walkthrough for this problem. And the class is online.

    How do I figure out what the N(t) and No values are.


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  3. #2  
    mvb
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    Quote Originally Posted by arina83 View Post
    I'm really stumped by this homework problem.

    N(t) = No (1-e^(-0.0372t))

    Where N(t) is final concentration at time t. No is final concentration.

    How long does it take to get 85% of final concentration.

    I can't figure out how to find the answer.

    First I was thinking that N(t)= 85 and No=100, since I'm guessing it starts at 100% concentration.

    85=100(1-e^(-0.0372t)) divide by 100

    85/100=(1-e^-0.0372t)) take ln of both sides

    ln(85/100) = 1-(-0.0372t) solve for t

    ...
    The problem is in the last step that I kept in the quote. ln(1-e-x) is not 1+x. You need to isolate the exponential before you take the logarithm.

    Thanks for putting down what you have done so I could diagnose your problem and hopefully help prevent the same thing from happening again.


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  4. #3  
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    Quote Originally Posted by arina83 View Post
    I'm really stumped by this homework problem.

    N(t) = No (1-e^(-0.0372t))

    Where N(t) is final concentration at time t. No is final concentration.

    How long does it take to get 85% of final concentration.

    I can't figure out how to find the answer.

    First I was thinking that N(t)= 85 and No=100, since I'm guessing it starts at 100% concentration.
    Why guess? You are given the equation! Plug in t=0 to get the initial concentration, then let t --> infinity to find the final concentration.

    You might also benefit by roughly sketching the function that is given. You might discover that some things you have been assuming are just plain wrong. Visualizing the general shape of things will help you understand what's going on. Don't rely solely on the manipulation of equations.
    Lynx_Fox likes this.
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