Respuesta :
Using the exponential decay model; we calculate "k"
We know that "A" is half of A0
A = A0 e^(k× 5050)
A/A0 = e^(5050k)
0.5 = e^(5055k)
In (0.5) = 5055k
-0.69315 = 5055k
k = -0.0001371
To calculate how long it will take to decay to 86% of the original mass
0.86 = e^(-0.0001371t)
In (0.86) = -0.0001371t
-0.150823 = -0.0001371 t
t = 1100 hours
We know that "A" is half of A0
A = A0 e^(k× 5050)
A/A0 = e^(5050k)
0.5 = e^(5055k)
In (0.5) = 5055k
-0.69315 = 5055k
k = -0.0001371
To calculate how long it will take to decay to 86% of the original mass
0.86 = e^(-0.0001371t)
In (0.86) = -0.0001371t
-0.150823 = -0.0001371 t
t = 1100 hours
Radioactive decay is the process in which an unstable atomic nucleus loses its energy in the form of radiation. The time taken for the drug to decay is, t = 9.14 hrs.
The exponential decay model is used to determine that the rate of decay is directly proportional to the amount or quantity present. The equation of the model can be written as:
[tex]\text {A}_n &= \text{A}_0\text e^{kt}[/tex]
where,
- k = rate of decay in a negative number
- An = amount left after time
- Ao = initial amount
Substituting the values:
[tex]\begin{aligned}\text {A}_n &= \text{A}_0\text e^{kt}\\\\0.5 &= e^{-k}(42 \text {hrs})\\\\\text k&=0.0165 \text {hrs}\\\\\text {A}_n &= \text{A}_0\text e^{kt}\\\\0.86 &=\text{A}_0\text e^{kt}\\\\0.86 &= e^{-k}0.0165 \text (t)\\\\\end{aligned}[/tex]
- t = 9.14 hrs.
Therefore, the time required by the drug to decay is 9.14 hrs.
To know more about radioactive decay, refer tot he following link:
https://brainly.com/question/4118334?referrer=searchResults
