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Math Help - Exponential growth/decay equations & usage

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    Exponential growth/decay equations & usage

    In my book I am given the equation A(t) = Aoe^(kt) (for exponential growth) Where t equals time and k is a constant. However, I saw an equation on another site for compounded interest in which k was replaced by r, the rate of interest. When do you use which equation? And what about exponential decay?
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    Re: Exponential growth/decay equations & usage

    From your description I would say that both equations are identical. They've merely applied a different nametag to the constant.

    If k>0 then there is exponential growth. If k<0 there is exponential decay (towards zero).
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    Re: Exponential growth/decay equations & usage

    Quote Originally Posted by benny92000 View Post
    In my book I am given the equation A(t) = Aoe^(kt) (for exponential growth) Where t equals time and k is a constant. However, I saw an equation on another site for compounded interest in which k was replaced by r, the rate of interest. When do you use which equation? And what about exponential decay?
    The equations are the same. r and k are constants with dimension 1/TIME. Different fields tend to use different symbols but they all refer to a constant. For example you'll see \lambda used as a decay constant in radioactivity. A good book will define it's symbols immediately before/after introducing them.

    Whether it's growth or decay depends whether or not there is a minus sign since the constant in the exponent is usually taken to be a positive constant. If it's there then you have decay, if not then it's growth. Below is an example

    Radioactive decay is given by the formula N = N_0e^{-\lambda t} where N is the number of nuclei at any given time, N_0 is the initial number of nuclei (when t=0), \lambda is a positive decay constant and t is time
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