The half-life of carbon-14 is about 5,730 years. A tree fossil was estimated to have about 4.2 picograms of carbon-14 when it died. (A picogram is a trillionth of a gram.) The fossil now has about 0.5 picogram of carbon-14. About how many years ago did the tree die? Show your reasoning.

17,190 years

Explanation:

Half life = 5,730 years

Initial amount = 4.2 picograms

Present amount = About 0.5 picograms

Number of half lives = ?

Before proceeding;

The half life  a material is simply the amount of time it takes for half of that material to decay.

4.2 --> 2.1 (First Half life)

2.1 --> 1.05 (Second Half life)

1.05 --> 0.525 (Third Half life)

It takes three half lives to reach it's present mass. This means number of years passed =  3 x 5,730 years = 17,190 years