Answer:
The half life of the substance is 6.0 days.
Step-by-step explanation:
The initial equation for the initial mass and mass at time t is;
N = [tex]N_{0}[/tex] [tex]e^{-kt}[/tex]
Where N is the mass at time t, [tex]N_{0}[/tex] is the initial mass, k is the constant and t is the half life. After the half life i.e t,
So that at a given time t, [tex]N_{0}[/tex] = 33 grams and N = 16.5 grams
⇒ 16.5 = 33 [tex]e^{-kt}[/tex]
16.5 = [tex]\frac{33}{e^{kt} }[/tex]
cross multiply, we have;
[tex]e^{kt}[/tex] = [tex]\frac{33}{16.5}[/tex]
[tex]e^{kt}[/tex] = 2
Find the natural logarithm of both sides,
ln [tex]e^{kt}[/tex] = ln2
kt = ln2
⇒ t = [tex]\frac{ln2}{k}[/tex]
t = [tex]\frac{0.6932}{0.1142}[/tex]
t = 6.07
The half life of the substance is 6.0 days.
