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Math Help - Exponents and Logarithms-- Exponent question

  1. #1
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    Exponents and Logarithms-- Exponent question

    Hi guys i just started this new unit, have a few question not having learned about logarithms, What would the formula look like?

    1) It is estimated that 30% of a certain substance decays in 20 hours. what is the half life of the substance.
    -- This is what i do to solve Y= AB^x- 50%=100%(100-30%=70 or .7%)^T = .5%=(.7)^T What is T in this case and how do i incorporate the 20 hours into this question? as well did i use the data given in the question correctly?

    Thanks in advance.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Exponents and Logarithms-- Exponent question

    I would set the problem up as follows:

    A(t)=A_0e^{-kt} where A_0 is the initial amount, and t is measured in hours.

    Now, we are told that when t=20 we have A(t)=0.7A_0 and this gives us:

    A(20)=A_0e^{-20k}=0.7A_0\,\therefore\,e^{-20k}=0.7

    Now, solve this for k by converting from exponential to logarithmic form, then substitute into the original function. Then equate this to 0.5A_0 and solve for t. What do you find?
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    Re: Exponents and Logarithms-- Exponent question

    I have not learned about logarithms so i dont know what that form is. Would i need to know about logs to solve?
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    MHF Contributor MarkFL's Avatar
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    Re: Exponents and Logarithms-- Exponent question

    I find it hard to conceive of being assigned a problem like this without first being taught about logarithms, and how to convert an equation from exponential to logarithmic form.

    \log_a(b)=c implies a^c=b
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    Re: Exponents and Logarithms-- Exponent question

    It seems your correct my teacher assigned me problems that i could not solve, Now that i have moved on in the chapter i am starting to learn about logs.

    Question though while solving exponential equations
    1)Sqrt(256)^5 / Sqrt(64)^6 -- when solving that i dont get one step how to i get rid of those sqrts? my teacher does a step where the sqrts go away and are left with [(256)^1/5] / [(64)^1/6]

    After that i can go from there but i dont get that step any help would be appreciated. As well thanks for your prompt replies MarkFL I hit the thanks button.
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