Final answer:
The age of the bowl is approximately 5730 years, based on it having only 40% remaining and using the half-life of 5730 years for ⁻4C.
Step-by-step explanation:
The half-life of ⁻4C is approximately 5730 years. In this case, we're given that only 40% of the bowl remains. Using the half-life formula, we can calculate the age of the bowl.
- Start with the original amount of the bowl, which is 100%.
- Since 40% remains, the amount that has decayed is 100% - 40% = 60%.
- Divide the amount that has decayed (60%) by the original amount (100%) to get the fraction remaining: 60% ÷ 100% = 0.6.
- Now, substitute the value for the half-life (5730 years) into the equation: (0.6) = (1/2)^n
- Solve for n by taking the logarithm of both sides: log((0.6)) = n * log((1/2))
- Divide both sides by log((1/2)) to isolate n: n = log((0.6)) / log((1/2))
- Use a logarithm calculator to find the value of n, which represents the number of half-lives: n = 0.51082
- Round n to the nearest whole number to get the number of half-lives: n ≈ 1.
- Multiply the number of half-lives by the half-life (5730 years) to get the age of the bowl: 1 * 5730 years = 5730 years.