# 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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