Answer:
Half life period = 43.11 days
Step-by-step explanation:
A sample substance has been taken for the use of drug research.
Weight of the substance taken = 0.25 gram
We have to use the formula of exponential decay to find the half life period of the substance.
Formula for the decay is [tex]A_{t}=A_{0}e^{-kt}[/tex]
Where [tex]A_{0}[/tex] is the weight of the substance taken initially
[tex]A_{t}[/tex] is the quantity remained after t time
and t = time
Now we have to find the half life life period
[tex]A_{t}[/tex] = [tex]\frac{0.25}{2}=.0125[/tex]
and [tex]A_{0}=25[/tex]
By putting these values in the formula
0.125 = 25[tex]e^{-0.1229t}[/tex]
[tex]e^{-0.1229t}[/tex] = [tex]\frac{0.125}{25}[/tex]
[tex]e^{-0.1229t}[/tex] = 0.005
Now we take natural log on both the sides of the equation
[tex]ln(e^{-0.1229t})=ln(.005)[/tex]
-0.1229t(lne) = -5.2983
0.1229t = 5.2983
t = [tex]\frac{5.2983}{0.1229}=43.11 days[/tex]≈ 43.10 days
Therefore, half life period of the substance is 43.10 days
