Answer:
The age of this sample is 13,417 years.
Step-by-step explanation:
The amount of carbon 14 present in a sample after t years is given by the following equation:
[tex]C(t) = C_{0}e^{-0.00012t}[/tex]
Estimate the age of a sample of wood discoverd by a arecheologist if the carbon level in the sampleis only 20% of it orginal carbon 14 level.
The problem asks us to find the value of t when
[tex]C(t) = 0.2C_{0}[/tex]
So:
[tex]C(t) = C_{0}e^{-0.00012t}[/tex]
[tex]0.2C_{0} = C_{0}e^{-0.00012t}[/tex]
[tex]e^{-0.00012t} = \frac{0.2C_{0}}{C_{0}}[/tex]
[tex]e^{-0.00012t} = 0.2[/tex]
[tex]ln e^{-0.00012t} = ln 0.2[/tex]
[tex]-0.00012t = -1.61[/tex]
[tex]0.00012t = 1.61[/tex]
[tex]t = \frac{1.61}{0.00012}[/tex]
[tex]t = 13,416.7[/tex]
The age of this sample is 13,417 years.
