## donnie1999 one year ago Situation: An archaeologist in turkey discovers a spear head that contains 32% of its original amount of c-14. N= Noe^-kt No= initial amount of C-14 at time t t= time, in years k= 0.0001 Find the age of the spear head to the nearest year.

1. donnie1999

@crissyyyxoxo

2. donnie1999

@aloud

3. anonymous

@phi

4. phi

start with $N= N_0e^{-kt}$ N is how much you have now, N0 is how much you started with. if we divide both sides by N0, you have $\frac{N}{N_0} = e^{-kt}$ N/N0 is the fraction we now have left. They tell us this is 32%, which means 32/100 or 0.32 also, they tell us k= 0.0001 put those numbers into the equation $0.32= e^{-0.0001\cdot t}$

5. phi

I would "take the natural log" of both sides as the next step.

6. donnie1999

whats that?

7. phi

If you are doing this type of problem, they assume you know about logarithms

8. donnie1999

@phi I am kind of clueless to these types of questions I was hoping you could help me out a little more.

9. phi

natural log , written ln means "exponent of base e" for example, if you write $e^x$ the natural log of that $\ln\left(e^x\right) = x$ is the exponent

10. phi

you want to use that idea on your equation to "get" the exponent -0.0001*t so write ln ( e^-0.0001*t) but because it is an equation, do the same to the other side, and write ln(0.32) now simplify the right-hand side using the rule: ln( e^stuff) simplifies to stuff