Question

Ytterbium decays 50% every 4.2 days. How much of an 80g sample would be left after 54.6 days? Use exponential decay formula.

Answer 1

Answer: Option E

$0.120\ g$

Step-by-step explanation:

The exponential decay formula is:

$C (t) = pe^ {-rt}$

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:

$p = 80\ g\\\\r=\frac{50\%}{100\%}\\\\r=0.5$

t is the time in units of 4.2 days

Then

$C(t) = 80e^{-0.5t}$

We want to calculate the amount of Ytterbium in 54.6 days.

Then as t is the time in units of 4.2 days

$t = \frac{54.6}{4.2} = 13\\\\t = 13$

Finally

$C(t=13) = 80e^{-0.5*13}$

$C(t) = 0.120\ g$