# 9th Grade Problem Solving Question

• September 22nd 2009, 11:51 PM
asaver
I need help with a homework question I was given. I have no idea if I’m meant to use a graph, equation or something else.

I have to find the age (in carbon-14 half lives) of a sample with a rate of disintegration of C-14 of .11 disintegrations/min/gram.

Basically I have to find x when y is .11

Half Life (x) Disintegration rate (y)
0................... 16
1................... 8
2................... 4
3................... 2
4................... 1
5................... 0.5
6................... 0.25
7................... 0.125
8................... 0.0625

(Note 1 C-14 Half-Life = 5730 Years before present)
• September 23rd 2009, 12:04 AM
Quote:

Originally Posted by asaver
I need help with a homework question I was given. I have no idea if I’m meant to use a graph, equation or something else.

I have to find the age (in carbon-14 half lives) of a sample with a rate of disintegration of C-14 of .11 disintegrations/min/gram.

Basically I have to find x when y is .11

Half Life (x) Disintegration rate (y)
0................... 16
1................... 8
2................... 4
3................... 2
4................... 1
5................... 0.5
6................... 0.25
7................... 0.125
8................... 0.0625

(Note 1 C-14 Half-Life = 5730 Years before present)

Hi ..

You can look at its pattern

$(0,2^4) , (1,2^3) , (2,2^2) , (3,2^1) , ...$

$(0,2^{4-0}) , (1,2^{4-1}) , ...$

y=2 to the power of 4 minus its 'x' .

$y=2^{4-x}$

so when y is 0.11 , $0.11=2^{4-x}$

Then calculate $\ln 0.11 = (4-x)\ln 2$

Can you continue ?
• September 23rd 2009, 12:31 AM
asaver
x = 4 - .11/2
idk
???
• September 23rd 2009, 02:32 AM
Quote:

Originally Posted by asaver
x = 4 - .11/2
idk
???

i don understand what you did ..

$4-x=\frac{\ln 0.11}{\ln 2}$

$4-x=-3.184$

$
x=7.184
$