Answer:
41.79 hours
Step-by-step explanation:
The Half-time Decay Formula: [tex]N=N_0(\frac{1}{2})^\frac{t}{d}[/tex]
Where [tex]N_0[/tex] is the original number, and t = time, and d = time it takes to half
18 would be d
100 would be [tex]N_0[/tex]
and 20 would be N
[tex]20=100(\frac{1}{2})^\frac{t}{18}[/tex]
[tex]0.2=(\frac{1}{2})^\frac{t}{18}[/tex]
[tex]log_\frac{1}{2}0.2=\frac{t}{18}[/tex]
[tex]18* log_\frac{1}{2}0.2=t[/tex]
[tex]18* \frac{log_{10}0.2}{log_{10}\frac{1}{2}}=t[/tex]
= 41.79470571
