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Situation:
A 8 gram sample of a substance that's a
by-product of fireworks has a k-value of
0.1001.
N = Noe-kt
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

Answer :

The half life of the substance is 6.92 days.

What is the Half life  ?

Half life can be defined as the time required to reduce the concentration to half of its initial value.

Here the equation given is

[tex]\rm N = N_o e^{-kt}[/tex]

The concentration will reduce to half therefore

[tex]\rm N= \dfrac{N_o}{2}[/tex]

so,

[tex]\rm 39/2 = 39 e^{- 0.1001 * t_{1/2}}[/tex]

ln 0.5 = - 0.1001 * t(1/2)

-0.693 = -.1001 * t(1/2)

t(1/2) = 6.92 days.

Therefore the half life of the substance is 6.92 days.

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