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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????

Verified Answer :

LammettHash

The decay model is given as

\(N=N_0e^{-Kt}\)

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 \(t\) such that \(N=\dfrac{N_0}2\). Substituting into the model, you have

\(\dfrac12=e^{-Kt}\)

You can solve for \(t\) now.

\(\dfrac12=e^{-Kt}\)
\(\implies\ln\dfrac12=\ln e^{-Kt}\)
\(\implies-\ln2=-Kt\ln e\)
\(\implies\dfrac{\ln2}K=t\approx5.7523\text{ days}\)

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