Question

Situation:

A 33 gram sample of a substance that's
used to detect explosives has a k-value
of 0.1473.
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

Find the substances half life, and days. Round your answer to the nearest 10th

Answer 1

4.7

Explanation:

Answer 2

Half life = 4.7 days

Explanation:

Formula to get the final amount of the substance after the time 't',

`N_t=N_0e^(-kt)`

Here,
`N_t` = Final amount of the substance

`N_0` = Initial amount

k = decay constant

t = Duration or time

Now by substituting the values in the formula,

`N_t=N_0e^(-0.1473t)`

If
`N_t=(1)/(2)(N_0)` [For half life]

`(1)/(2)(N_0)=N_0e^(-0.1473t)`

`(1)/(2)=e^(-0.1473t)`

`2=e^(0.1473t)`

ln(2) =
`\text{ln}(e^(0.1473t))`

0.69315 = 0.1473t

t = 4.71 days

t ≈ 4.7 days

Therefore, half life of the substance is 4.7 days.