Answer: Option E
[tex]0.120\ g[/tex]
Step-by-step explanation:
The exponential decay formula is:
[tex]C (t) = pe^ {-rt}[/tex]
Where p is the initial amount of Ytterbium
r is the rate of decrease
C(t) is the amount of Ytterbium in grams as a function of time
t is the time in days
In this problem:
[tex]p = 80\ g\\\\r=\frac{50\%}{100\%}\\\\r=0.5[/tex]
t is the time in units of 4.2 days
Then
[tex]C(t) = 80e^{-0.5t}[/tex]
We want to calculate the amount of Ytterbium in 54.6 days.
Then as t is the time in units of 4.2 days
[tex]t = \frac{54.6}{4.2} = 13\\\\t = 13[/tex]
Finally
[tex]C(t=13) = 80e^{-0.5*13}[/tex]
[tex]C(t) = 0.120\ g[/tex]
