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The charcoal from a tree killed in the volcanic eruption that formed a crater is measured for carbon-14. If the half-life of carbon-14 is 5700 years, (a) Create a mathematical model for the proportion of carbon-14 found in the tree. (b) If the volcanic eruption happened 20,000 years ago, what proportion of C-14 is left in the tree? (round to the nearest year). (c) A nearby tree that died in the same eruption contains 0.002 g of

`C-14`

. How many grams of

`C-14`

did this tree contain prior to the eruption?