Question

The radioactive isotope Bismuth-210 has a half-life of 5 days. How many days does it take for 87.5% of a given amount to decay?

Answer 1

A half-life of five days means half of the original amount of the isotope remains after 5 days, i.e.
\[\frac{1}{2}=e^{5k}\]
Find the relative decay factor \(k\).

After that, you want to find the time it takes for the amount to decay to 87.5% its original amount, i.e 0.875:
\[0.875=e^{kt}\]
Plug in the \(k\) you found earlier and solve for \(t\).

Answer 2

so what is the answer. im struggling

Answer 3

http://www.wolframalpha.com/input/?i=k%3DLog [.5]%2F5%2C+.875%3DExp[kt]

Answer 4

For whatever reason, the URL is getting cut short... Copy and paste.

Answer 5

so 0.96?

Answer 6

Yes