Question

A student in Greece discovers a pottery bowl that contains 48% of its original amount of C-14. Find the age of the pottery bowl to the nearest year. N=N0e*kt N0= initial amount of C=14 (at time t=0) N= amount of C-14 at time t t= time, in years k=0.0001

Answer 1

So you know that N/N0 = .48 and k=.00001 (and e=2.718)

Your equation becomes:
.48 = 2.718*(.00001*t)

NOTE: you probably mean \[e ^{kt}\] right?

Answer 2

Yes i think

Answer 3

then it would be \[.48=(2.718)^{.00001t}\]

Answer 4

Does that help? Or do you still need help?

Answer 5

It says e^-kt actually

Answer 6

ok, so \[.48=2.718^{-.0001t}\]

Answer 7

do you know how to solve for t?

Answer 8

Nope.

Answer 9

ok, so, I'm guessing that you're in pre-calc or something? to remove e, you have to take the natural log (ln) of both sides of the equation

Answer 10

I got -7340.4528405

Answer 11

Let me check

Answer 12

I got 7339.691 (probably just rounding difference, and don't forget the negative sign on k)

Answer 13

Wait so it's positive?

Answer 14

And would that round up to 7340?

Answer 15

yep, because you can't have negative years, right? So it would be 7340 years. (I think)

Answer 16

yes, because at 7339 years, it wouldn't have degraded all the way yet. So 7340 is the right answer

Answer 17

That makes sense, haha. Thank you for helping. I'm awful when it comes to turning a word problem into an equation.

Answer 18

no problem! glad to help

Answer 19

would you be willing to help me on 3 others..?

Answer 20

sure, shoot.

Answer 21

An archaeologist in Turkey discovers a spear head that contains 63% of its original amount of C-14. Find the age of the spear head to the nearest year.

Answer 22

With the same equation?

Answer 23

and the same k?

Answer 24

Yes

Answer 25

Well, what would N/N0 be in this equation?

Answer 26

It's the same formula, I just can't make an equation. If you showed me I could solve it.

Answer 27

I know, I'm trying to get you to do it. In the last equation, we knew that there was 48% of the original substance remaining, so we knew that Ncurrent/Noriginal (N/N0) was .48 or 48%.

So what would N/N0 be in this case where there is 68% of the original substance remaining?

Answer 28

.68

Answer 29

right, so just solve for .68 in the same equation

\[.68=e ^{-.0001t}\]

where e is still the constant 2.718

Answer 30

understand how I got that?

Answer 31

Well kinda, I don't understand the 2.718..?

Answer 32

But I got 3857.02

Answer 33

http://en.wikipedia.org/wiki/E_%28mathematical_constant%29

e is a mathematical constant, (like pi=3.1415926....) it's based on circle geometry. It's safe to estimate e=2.718

Answer 34

Oh! Ok thanks I didn't know that.

Answer 35

No problem, does that help you with the other ones? (I got 3856.625, so 3857, don't forget to round up to the nearest whole number!)

Answer 36

That does, but hang on the other ones might be different..

Answer 37

Would 14=2.718^(0.1481t) simplify to 18?

Answer 38

If you're still rounding up, then yes.

Answer 39

BUT

Answer 40

In this case, you have N0=14. What is the problem asking you to solve for?

Answer 41

The substances half life in days. And to round to the nearest 10th.

Answer 42

So you want to know how long it takes to get to N=7 (where only half of the 14 grams are left)

Can you fix your equation?

Answer 43

7=2.718^(0.1481t)

Answer 44

mm, close, you forgot N0

Answer 45

Ok then I'm confused ;_;

Answer 46

Ok, so you have N=N0*e^(-kt) right?

You know that you start with 14 grams so:

N=14*e^(-kt)

Then you know that you want to know how long it takes to get to half of 14 grams (=14/2=7) so:

7=14*e^(-kt)

Plug in your constants:

7=14*2.718^(-.1481t)

Yes?

Answer 47

Oh, ok. I will solve now.

Answer 48

4.68?

Answer 49

yes, which would round to .....? (unless you're allowed to do decimals)

Answer 50

Well it said on this one to round to the nearest tenth.

Answer 51

oh right, so 4.7

Answer 52

.68 would be to the nearest hundredth

Answer 53

Oh ok :) Thank you.

Answer 54

no problem, anything else?

Answer 55

Maybe, not sure yet.

Answer 56

I will post on here if I have something else.

Answer 57

Ok, I have to get back to work. I'll try to check back, but no promises. You clearly get it, just keep truckin!