Radiocarbon dating is a process where the amount of carbon-14 in an object is me

Question

Radiocarbon dating is a process where the amount of carbon-14 in an object is measured to determine its age; it is often used to date historical artifacts unearthed by archeologists. The amount of carbon-14 in a sample decays exponentially with time, such that the amount halves every 5730 years. Let C(t) be the fraction of the carbon-14 originally present remaining after t. years. Write down a formula for C(t). A picture, supposedly painted by Vermeer (1632-1675), is offered for sale. Tests indicate that 99.5% of the carbon-14 originally present remains. Would you buy it? Explain your answer.

Explanation / Answer

We have to use the following formula

N(t)= N0ekt

Where N(t) is the amount of carbon after t years

Let initial amount be xgm

x/2=x e5730t

ln(1/2)=5730k

k=(ln(1/2))/5730

N(t)=N0et (ln(1/2))/5730

N(t)=N0(1/2)t/5730

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