Carbon-14 has a half-life of 5720 years and this is a first order reaction. if a piece of wood has converted 75% of the carbon-14, then how old is it?

a) 11440 years
b) 2375 years
c) 4750 years
d) 4290 years
e) 1430 years

The amount of the substance (At) at any time t is calculated through the equation,
                                  At = (A0)(e^-kt)
where A0 is the initial amount and k is constant. 

For the half-life,
                              ln (At / A0) = ln 0.5 = -k(5270 years)
The value of k is 1.3153x10^-4 / year.
Substituting this value to the same equation, where At = 0.25A0
                                    ln 0.25 = -(1.3153 x 10^-4)(t)
The value of t from this equation is 10540 years. The closest value to this is letter A. 
                                

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