Question

Situation: a 25 gram sample of a substance that’s used for drug research has a K-value of 0.1205

Answer 1

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.

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