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Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248
Textbook Problem

Carbon Dating A fossil contains 4.06 grams of carbon 14. It is estimated that the fossil originally contained 46 grams of carbon 14. By calculating the amount left after 5,000 years, 10,000 years, …, 35,000 years, estimate the age of the sample to the nearest 5,000 years. (Refer to the formula for C ( t ) in Example 7.)

To determine

To calculate: The age of the sample to the nearest 5000 years by calculating the amount left after 5000 years, 10,000 years, …, 35,000 years using the formula for amount, A of carbon 14 is approximated by C(t)=A(0.999879)t where t is time in years if a fossil originally contained 46 grams of carbon 14 and the fossil contains 4.06 grams of carbon 14.

Explanation

Given Information:

The formula for amount, A of carbon 14 is approximated by C(t)=A(0.999879)t where t is time in years if a fossil originally contained 46 grams of carbon 14 and the fossil contains 4.06 grams of carbon 14.

Calculation:

Consider the original amount of carbon 14, A=46 grams and amount left is C=4.06 grams

Evaluate the t by substituting the values in the formula C(t)=A(0.999879)t as;

4.06=46(0.999879)t

Evaluate the value of amount of carbon 14 left after 5000 years by substituting, t=5,000 as;

C(5000)=46(0.999879)5000=46×0.54625.1

Evaluate the value of amount of carbon 14 left after 10000 years by substituting, t=10,000 as;

C(10000)=46(0.999879)10000=46×0.298213.7

Evaluate the value of amount of carbon 14 left after 15000 years by substituting, t=15,000 as;

C(15000)=46(0.999879)15000=46×0

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