Question

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.

Answer 1

@crissyyyxoxo

Answer 2

@aloud

Answer 3

@phi

Answer 4

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
\[ 0.32= e^{-0.0001\cdot t} \]

Answer 5

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

Answer 6

whats that?

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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