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Is the rate constant in the rate equation equivalent to that in the arrhenius equation?

Does the arrhenius equation describe the overall rate of reaction or can be interpreted to compute the rate of forward reaction and backward reaction respectively? If it could be employed to deal with both sides separately, then I know why the decay of radioactive substance has a constant half-life, otherwise, it still seems to be an enigma to me though after exhausting search in the web.

 

Please help

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[math]Rate = k[A]^a[ B]^b[/math] is the rate equation for reaction A + B and depending on values of a and b, which will determine the order of reaction, you get various half life equations, for example, for zero-order reaction half life is of one form while for first order reaction is different and so again for third order reaction (cbb latexing you examples here you can look it up on: http://en.wikipedia.org/wiki/Rate_equation :) ). And as for Arrhenius equation, I believe it is the same k indeed.

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