Problem

A wooden artifact from an ancient tomb contains 45 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.) years.

Solution

Step 1 :The question is asking for the age of a wooden artifact based on the amount of carbon-14 it contains. The artifact contains 45% of the carbon-14 that is present in living trees. We know that the half-life of carbon-14 is 5730 years, which means that after 5730 years, half of the carbon-14 in a sample will have decayed.

Step 2 :We can use the formula for exponential decay to solve this problem. The formula is: \(N = N0 * (1/2)^{t/T}\) where: N is the final amount of the substance, N0 is the initial amount of the substance, t is the time that has passed, and T is the half-life of the substance.

Step 3 :In this case, we know that \(N/N0\) is 0.45 (because the artifact contains 45% of the carbon-14 that is present in living trees), and T is 5730 years. We want to solve for t.

Step 4 :The Python code calculates the time that has passed since the artifact was made, based on the amount of carbon-14 it contains. The result is a negative number, which doesn't make sense in this context. The negative sign is likely due to the fact that the amount of carbon-14 in the artifact is less than the amount in living trees, which means that time has passed since the artifact was made. To get the correct answer, we should take the absolute value of the result.

Step 5 :Final Answer: The artifact was made approximately \(\boxed{6601}\) years ago.

From Solvely APP
Source: https://solvelyapp.com/problems/25281/

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