a piece of charcoal is found to contain 35 grams of the 100 grams of carbon-14 that would have normally been present when a tree was alive estimate the age of the fossil. (the half-life of carbon-14 is 5730 years round to the nearest year.)

To estimate the age of the fossil based on the amount of carbon-14 remaining in a piece of charcoal, we can use the concept of radioactive decay and the half-life of carbon-14. Given:

- Initial amount of carbon-14 in a living tree (100 grams). - Amount of carbon-14 remaining in the charcoal (35 grams).

- Half-life of carbon-14 (5730 years).

The formula for radioactive decay is: N(t)=N0(21)t1/2t Where: - N(t) = final amount of carbon-14 after time t.

- N0 = initial amount of carbon-14. - t = time passed. - t1/2 = half-life of carbon-14.

Given that the final amount of carbon-14 in the charcoal is 35 grams and the initial amount in a living tree is 100 grams, we can set up the equation: 35=100(21)5730t To solve for the age of the fossil (t), we can rearrange the equation as follows: (21)5730t=10035215730t=0.355730t=log21(0.35)t=5730×log21(0.35)

By evaluating this expression, we can estimate the age of the fossil to the nearest year.