Carbon Dating A fossil originally contained 104 grams of carbon 14. Refer...

Carbon Dating A fossil originally contained 104 grams of carbon 14. Refer to the formula for C(t) in Example 7 and estimate the amount of carbon 14 left in the sample after 10,000 years, 20,000 years, and 30,000 years. HINT [See Example 7.]

Example 7: Exponential Decay: Carbon Dating

The amount of carbon 14 remaining in a sample that originally contained A grams is approximately

where t is time in years.

a. What percentage of the original amount remains after one year? After two years?

b. Graph the function C for a sample originally containing 50g of carbon 14, and use your graph to estimate how long, to the nearest 1,000 years, it takes for half the original carbon 14 to decay.

c. A fossilized plant unearthed in an archaeological dig contains 0.50 gram of carbon 14 and is known to be 50,000 years old. How much carbon 14 did the plant originally contain?