A 30 gram sample of a substance that's used to sterilize surgical instruments has a k-value of 0.1253. Find the substance's half life in days, round to the nearest tenth.

Initial Amount: Ao=30 grams

k=0.1253

Amount after t days: A (t)

A (t) = Ao*e^ (-kt)

Half-life is the time t=T when A (t) = Ao/2:

Ao/2=Ao*e^ (-0.1253T)

Dividing both side by Ao:

1/2=e^ (-0.1253T)

Applying natural logarithm (ln) to both sides of the equation:

ln (1/2) = ln[e^ (-0.1253T) ]

ln1-ln2=-0.1253T*lne

0-ln2=-0.1253T*1

-ln2=-0.1253T

Dividing both sides of the equation by - 0.1253:

-ln2 / (-0.1253) = T

T=ln2/0.1253

T=0.693147181/0.1253

T=5.531900882

T=5.5 days

The substance's half life is 5.5 days.