   Chapter 2.3, Problem 39E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Carbon Dating The amount of carbon 14 remaining in a sample that originally contained A grams is given by C ( t ) = A ( 0.999879 ) t where t is time in years. If tests on a fossilized skull reveal that 99.95% of the carbon 14 has decayed, how old, to the nearest 1,000 years, is the skull?

To determine

To calculate: The age of the skull if the test reveal that 99.95% of the carbon of the fossilized skull has decayed.

Explanation

Given Information:

The amount of the carbon 14 remaining in a sample that initially has A gram is given by,

C(t)=A(0.999879)t

Total 99.95% of the carbon of the fossilized skull has decayed.

Formula used:

The logarithmic relation of indices is,

logbx=xlogb

Calculation:

Consider the amount of the carbon 14 remaining in a sample that initially has A gram,

C(t)=A(0.999879)t

As the total 99.95% of the carbon of the fossilized skull has decayed. Thus, remaining percentage of the carbon 14 in the skull is,

(10099.95)%=0.05%

Since, the skull initial has 100% carbon 14 atoms. Therefore, A=100.

Now substitute C(t)=0.05 and A=100 in the formula C(t)=A(0.999879)t,

0.05=100(0.999879)t

Divide both side by 100,

0

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