Question

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.

Answer 1

The substance's half-life is 6.77 days

N = $N_{0} e^{-kT}$
Where,
$N_{0}$ = 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$T_{ \frac{1}{2}}$ = ?

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

N ($T_{ \frac{1}{2}}$) = $\frac{N}{2}$

⇒ $\frac{39}{2}$ = 39 $e^{- 0.1024 t}$

⇒ ln 0.5 = -0.1024t

⇒ t = 6.77 days