anonymous 5 years ago can anyone help me with exponential decay?

1. anonymous

why not?

2. anonymous

$Q=Q_0 e^{-rt}$

3. anonymous

Situation: a 42 gram sample of substance that's used to treat thyroid disorders has a k-value of 0.124 Find the substance's half-life, in days. Round your answer to the nearest tenth.

4. anonymous

i am assuming "k-value" is r, so the equation is $Q=Q_0 e^{-.124t}$ and half life means how long before you have half of your original amount. it doesn't matter what the original amount is.

5. anonymous

so set $e^{-.124t}=\frac{1}{2}$ and solve for t.

6. anonymous

$e^{-.124t}=\frac{1}{2}$ $-.124t=ln(\frac{1}{2})$ $t=\frac{ln(\frac{1}{2})}{-.124}$

7. anonymous

i get 5.59 rounded. to the nearest tenth it would be 5.6 hope the steps are clear. if not let me know.

8. anonymous

thank you!

9. anonymous

oh wait. i did not use the 42 grams part, so maybe i don't know what k-value is. can you tell me what k-value means exaclty?

10. anonymous

11. anonymous

whew so k-value is the rate of decay and the 42 was a red herring. good!

12. anonymous

5.6