Exponential decay

Show that if a radioactive substance has a half life of T, then the corresponding exponential decay function can be written as y=y0e^kt

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  1. amountleft=akmountoriginal (1/2)^t

    left/original= (1/2)^t

    taking the ln of each side
    ln(left/orig)=t ln(.5)=kt

    now take the antilog of each side
    left/orig=e^kt
    left=yo*e^kt
    so what is k?
    if left/yo=e^kt
    at 1/2= e^k*T
    ln of each side
    .693=kT
    k= .693/T

    so the equation is of the form...
    y= yo e^ln.5 * t/T

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