Answer:
4.7935 days
Step-by-step explanation:
The expression that describes exponential decay is the following:
N(t) = No * [tex]e^{-kt}[/tex]
Where N(t) is the mass of the substance after a period t of time.
No is the original amount of substance
k is the relative decay rate and t is the period of time elapsed.
The half life is the period of time after which the amount of substance has decreased by half.
We can issolate t in the expression, using the properties of logarithms:
[tex]\frac{N(t)}{No}[/tex]=[tex]e^{-kt}[/tex]
ln([tex]\frac{N(t)}{No}[/tex]) = -k*t
t = - ln([tex]\frac{N(t)}{No}[/tex])/k = - ln([tex]\frac{1}{2}[/tex])/0.1446 = 4.7935 days.
