A wooden artifact from an archaeological dig contains 90 percent of the Carbon-14 that is half-life of Carbon-14 is 5730 years.) yr

Step 1 ：The problem is asking to find the age of a wooden artifact from an archaeological dig. The artifact contains 90 percent of the Carbon-14 that is present in living wood. The half-life of Carbon-14 is 5730 years.

Step 2 ：We can use the formula for calculating the age based on half-life: \(t = \frac{T_{1/2}}{\ln(2)} \times \ln(\frac{N_0}{N})\), where \(t\) is the age of the sample, \(T_{1/2}\) is the half-life of the isotope, \(N_0\) is the initial quantity of the substance, and \(N\) is the remaining quantity of the substance.

Step 3 ：In this case, \(T_{1/2} = 5730\) years, and \(\frac{N_0}{N} = \frac{100}{90} = 1.1111\) (since the artifact contains 90 percent of the Carbon-14).

Step 4 ：Substituting these values into the formula, we get \(t = \frac{5730}{\ln(2)} \times \ln(1.1111)\).

Step 5 ：Calculating the above expression, we find that the age of the artifact is approximately 871 years.

Step 6 ：Final Answer: The age of the wooden artifact is approximately \(\boxed{871}\) years.