Answer:
[tex]\frac{N(t)}{N_{0}}=0.17830731692
[/tex]
Explanation:
There are many formulas that can describe the exponential decay of a substance. For example, one of the formulas we could use for the quantity that still remains after a time t, given an original quantity [tex]N_0[/tex] and a half-life of [tex]t_{1/2}[/tex] is:
[tex]N(t)=N_{0}(\frac{1}{2})^{t/t_{1/2}}[/tex]
We want to calculate what fraction of the original shipment would still we have, that is, [tex]\frac{N(t)}{N_{0}}[/tex]
This is why it is useful to use the formula already written, now we can just calculate:
[tex]\frac{N(t)}{N_{0}}=(\frac{1}{2})^{t/t_{1/2}}=(\frac{1}{2})^{20days/8.04days}=0.17830731692[/tex], which means that around 17.83% of the original substance has not decayed yet.
