The age of the fossil using carbon dating comes out to be 19188.21 years.
What is the formula for carbon-14 dating?
The formula for carbon-14 dating is given by:
[tex]A = Ie^{kt}[/tex]
Where A = Amount
I =initial amount
k=constant of growth or decay
[tex]\frac{A}{I} =e^{kt}[/tex]
In the case of a half-life
[tex]0.5=e^{kt_{1/2} }[/tex]
[tex]ln 0.5 = k\frac{t_{1/2} }{2}[/tex]
We know the half-life of carbon-14 is 5700 years i.e. [tex]t_{1/2} =5700[/tex]
So, [tex]ln 0.5 = k\frac{5700}{2}[/tex]
[tex]k=-0.00024[/tex]
According to the question
[tex]ln0.1 = -0.00024*\frac{t}{2}[/tex]
[tex]2ln0.1 = -0.00024*t[/tex]
[tex]t = 19188.21[/tex] years.
Hence, The age of the fossil using carbon dating comes out to be 19188.21 years.
To get more about carbon dating visit:
https://brainly.com/question/15673495
