musicojada1
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Situation:

A 39 gram sample of a substance that's a by-product of fireworks has a k-value of 0.1024.

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
Find the substance's half-life, in days.

Round your answer to the nearest tenth.

Respuesta :

tiara143
The substance's half-life is 6.77 days

N = [tex] N_{0} e^{-kT} [/tex]
Where,
[tex] N_{0} [/tex] = 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

The, half life t[tex] T_{ \frac{1}{2}} [/tex] = ?

Then at half life, the sample will remain half., i.e.

N ([tex] T_{ \frac{1}{2}} [/tex]) = [tex] \frac{N}{2} [/tex]

⇒ [tex] \frac{39}{2} [/tex] = 39 [tex] e^{- 0.1024 t} [/tex]

⇒ ln 0.5 = -0.1024t

⇒ t = 6.77 days

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