the half-life of carbon-14 is 5,600 years. If 3% of C-14 is found today, find the age of the element. If 2% remains now, find the age of the element.

Question

anonymous · Answer

$$(\frac{1}{2})^{\frac{t}{5,600}}=.03$$ solve for $t$

lgbasallote · Answer

is that t/5600?

anonymous · Answer

you got this ? it take two steps

anonymous · Answer

$$\large (\frac{1}{2})^{\frac{t}{5,600}}=.03$$

lgbasallote · Answer

yeah..i wanted to make sure i didnt do any careless mistakes.

lgbasallote · Answer

ahh the same as i got! wonderful

anonymous · Answer

first change of base gives 
$$\frac{t}{56,000}=\frac{\ln(.03)}{\ln(.5)}$$ and then 
$$t=56,000\times \frac{\ln(.03)}{\ln(.5)}$$ and then a calculator

lgbasallote · Answer

im guessing for the other one it will be $$\huge (\frac 12)^{t/5600} = 0.02?$$

anonymous · Answer

although these days i guess you can do it calculator in one step,

anonymous · Answer

yup

lgbasallote · Answer

ahh wonderful. it seems i was right...i think...i dont recall my answers

and yeah we can use calculator for one step now..a lot has changed ever since you entered that cryogenic chamber