# Carbon-14 has a half life of 5730 years. If a shell is found and has 52% of its original Carbon-14, how old is it?

##### 2 Answers

Approximately

#### Explanation:

#-5730 * log_2(52/100) = -5730 * log(52/100)/log(2) ~~ 5406# years

The proportion of

#p(t) = 2^-t/(5730)#

where

Given that

#52/100 = 2^(-t/5730)#

Taking logs base

#log_2(52/100) = -t/5730#

So multiplying both sides by

#t = -5730*log_2(52/100)#

**Footnote**

The complexity of radiocarbon dating comes from two factors:

- The proportion of
#""^14C# to#""^12C# is very small to start with. - The proportion has been dramatically affected by factors like the industrial revolution, which replaced a significant portion (one third? one quarter?) of the
#CO_2# in the atmosphere with carbon dioxide generated from fossil fuels - which contain virtually no remaining#""^14C# . As a result the method needs calibration to provide accurate dates.

#### Explanation:

The expression for radioactive decay is:

Taking natural logs of both sides:

We can get the value of

Putting in the numbers: