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

Answer:

Half life = 4.7 days

Step-by-step 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 $N_t=\frac{1}{2}(N_0)$ [For half life]

$\frac{1}{2}(N_0)=N_0e^{-0.1473t}$

$\frac{1}{2}=e^{-0.1473t}$

$2=e^{0.1473t}$

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.

Answer 2

Answer:

4.7

Step-by-step explanation: