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Situation: a 25 gram sample of a substance that’s used for drug research has a K-value of 0.1205
N0(zero)= initial mass(at time t=0)
N= mass at time t
K= a positive constant that depends on the substance itself and on the units used to measure time
t= time, in days
Find the substances half-life, in days. Round your answer to the nearest tenths????

Respuesta :

LammettHash
The decay model is given as

[tex]N=N_0e^{-Kt}[/tex]

The substance's half-life is the time it takes for the substance to decay to half its original amount. In other words, it's the time [tex]t[/tex] such that [tex]N=\dfrac{N_0}2[/tex]. Substituting into the model, you have

[tex]\dfrac12=e^{-Kt}[/tex]

You can solve for [tex]t[/tex] now.

[tex]\dfrac12=e^{-Kt}[/tex]
[tex]\implies\ln\dfrac12=\ln e^{-Kt}[/tex]
[tex]\implies-\ln2=-Kt\ln e[/tex]
[tex]\implies\dfrac{\ln2}K=t\approx5.7523\text{ days}[/tex]

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