A 22 gram sample of a substance that's used to sterilize surgical instruments has a k-value of 0.138.

N=N0e^-kt
N0=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

What is the substance's half-life, in days rounded to the nearest tenth?

Question

A 22 gram sample of a substance that's used to sterilize surgical instruments has a k-value of 0.138.

N=N0e^-kt
N0=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

What is the substance's half-life, in days rounded to the nearest tenth?

holsteremission · Answer

The half-life is the time it takes for the substance to decay to half its original amount. This means if the half-life is $T$, then $N=\dfrac{N_0}{2}$ and the half-life is given by
$$\frac{1}{2}=e^{-kT}\implies T=\frac{1}{k}\ln2$$Plug in $k$ and you get your answer.