Question

a certain radioactive substance decays from 35,490 gm to 650 gm in 5 days. What is its half life?
.693 days
.866 days
1.600 days
.690 days

Answer 1

equation will be \[Q=35490e^{rt}\] where t is time in days. you know that when \[t=5\] \[Q=650\] so solve for r via
\[650=35490e^{5r}\]

\[\frac{650}{35490}=e^{5r}\]
\[ln(\frac{650}{35490}=5t\]
\[t=\frac{ln(\frac{650}{35490})}{5}\]

Answer 2

or roughtly -.8. so you want to know when
\[e^{-.8t}=\frac{1}{2}\]
and now solve for t:
\[-.8t=ln(\frac{1}{2})\]
\[t=\frac{ln(.5)}{-.8}\].

Answer 3

about .866 days from the calculator.

Answer 4

Wow thank you. The first equation was a little easier to understand.

Answer 5

first one?

Answer 6

perhaps the "half life" one was confusing. formula is always
\[Q(t)=Q_0e^{rt}\] and "half life" means the time it takes to get half the original amount. so if you start with \[Q_0\] then half of it is \[\frac{1}{2}Q_0\] and you would solve
\[\frac{1}{2}Q_0=Q_0e^{rt}\] for t
step number one is do divide both sides by
\[Q_0\] so you may as well start with
\[\frac{1}{2}=e^{rt}\]

Answer 7

or you can simply remember if the rate of decay is r, then half life is
\[\frac{ln(.5)}{-r}\] here i am assuming r is written as a decimal and also as positive, so say, for example, your substance decays at a rate of 3% per hour then r =.03