Answer:
35 hrs
Explanation:
half life of the substance [tex]t_{1/2 }[/tex] = 8.1 hr
initial amount [tex]N_{0}[/tex] = 75 g
The final amount [tex]N[/tex] = 3.9 g
The time elapsed [tex]t[/tex] = ?
we use the relationship
[tex]N[/tex] = [tex]N_{0}[/tex] [tex](\frac{1}{2} )^{\frac{t}{t_{1/2} } }[/tex]
substituting values, we have
3.9 = 75 x [tex]\frac{1}{2}^{\frac{t}{8.1} }[/tex]
0.052 = [tex]\frac{1}{2}^{\frac{t}{8.1} }[/tex]
take the log of both side
log 0.052 = log [tex]\frac{1}{2}^{\frac{t}{8.1} }[/tex]
log 0.052 = [tex]\frac{t}{8.1}[/tex] log 1/2
-1.284 = [tex]\frac{t}{8.1}[/tex] x -0.301
1.284 = 0.301t/8.1 =
1.284 = 0.0372t
t = 1.284/0.037 = 34.5 ≅ 35 hrs
