anonymous 5 years ago 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

1. anonymous

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

2. anonymous

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

3. anonymous

about .866 days from the calculator.

4. anonymous

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

5. anonymous

first one?

6. anonymous

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 $\frac{1}{2}=e^{rt}$

7. anonymous

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