Answer:
2,700 years
Explanation:
We were given the following details:
Half-life of carbon-14, T = 5600 years
78% of carbon-14 is left. This indicates that the amount of carbon-14 left is 78% of the initial amount:
[tex]0.78\times A_0[/tex]We will calculate the time since when the tree died as shown below:
[tex]\begin{gathered} 0.78\times A_0=A_0\times(0.5)^{\frac{t}{T}} \\ T=5600years \\ t=? \\ \text{Substitute the variables into the formula, we have:} \\ 0.78=(0.5)^{\frac{t}{5600}} \\ \text{Take the natural logarithm of both sides, we have:} \\ ln(0.78)=\frac{t}{5600}\times ln(0.5) \\ \text{Make ''t'' the subject of the formula, we have:} \\ t=5600\times\frac{ln(0.78)}{ln(0.5)} \\ t=5600\times0.35845397091 \\ t=2007.34223711\approx2007 \\ t=2,007years \end{gathered}[/tex]Therefore, the tree died 2,700 years ago
