Situation: A 46 gram sample of a substance that's a
by-product of fireworks has a k-value of
0.1374.
-kt
N = Noe
No = 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

5.0 days

Step-by-step explanation:

From the question given above, the following data were obtained:

Initial mass (N₀) = 46 g

Constant (K) = 0.1374 /day

Half life (t₁/₂) =?

The half life (t₁/₂) is related to the decay constant according to the following equation:

t₁/₂ = 0.693 / K

With the above equation, we can obtain the half-life of the substance as follow:

Constant (K) = 0.1374 /day

Half life (t₁/₂) =?

t₁/₂ = 0.693 / K

t₁/₂ = 0.693 / 0.1374

t₁/₂ = 5.04 ≈ 5.0 days

Thus, the half-life of the substance is 5.0 days