after 6.2 hours the dose will decay to 70% in your bloodstream.
We know that the half-life is 12 hours. Then the exponential relation for an initial dosage of A is:
[tex]D(t) = A*e^{-t*ln(2)/12h}[/tex]
If the dosage needs to decay to a 70% of the initial dosage, then we must have:
[tex]e^{-t*ln(2)/12h} = 0.7[/tex]
Now we need to solve that for t:
If we apply the natural logarithm in both sides, we get:
[tex]ln(e^{-t*ln(2)/12h}) = ln(0.7)\\\\-t*ln(2)/12h = ln(0.7)\\\\t = -ln(0.7)*12h/ln(2) = 6.2h[/tex]
So after 6.2 hours the dose will decay to 70% in your bloodstream.
If you want to learn more about half-life:
https://brainly.com/question/11152793
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