can anyone help me with exponential decay?

Question

anonymous · Answer

why not?

anonymous · Answer

$$Q=Q_0 e^{-rt}$$

anonymous · Answer

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.

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

thank you!

anonymous · Answer

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?

anonymous · Answer

that answer was correct

anonymous · Answer

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

anonymous · Answer

5.6