[填空题]
Radiocarbon dating can be used to estimate the age ofe1 1fo:zvu420orv jjt an artifact ma9cx6r et )155ioc4h*zz dsuk3n d4j hude of wood. Archeologists take a sample of wood from the artifact and measure the ratio,r k 4ud 5the 4)3z1incru 6ojsh5xcdz*9, of Carbon-1414 in the sample to Carbon-1414 in a living wood. The age, t, in years, is then estimated by using the equation
t=−$\frac{6000}{ln2}\times$lnr,[Age Model]
where 0.01A team of underwater archeologists found an ancient wooden shipwreck deep down in the Black Sea. A sample of wood is taken from the shipwreck to determine its age.
1.Find the age of the shipwreck if r=0.75.
In all wood samples, Carbon-14 decays over time. If r<0.01, there is insufficient amount of Carbon-14 left in the sample wood for its age estimate calculated by the age model to be reliable. t ≈
2.Find the oldest sample of wood for its age estimate found by the age model would just cease to be reliable. Give your answer to the nearest10000 years. t ≈
3.Using the age model, express r in terms of t.
4.Hence find r when t=7500, giving your answer correct to 2 decimal places. r ≈
