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Griffiths Pierce

10/05/2021 · Elementary School

The half-life of the radioactive isotope Carbon- \( 14 \) (present in all organic materials) is about \( 5730 \) years. 

a) Use the equation \( A ( t ) = A _ { 0 } e ^ { k t } \) to express the amount of Carbon- \( 14 \) left from an initial \( N \) milligrams as a 

function of time \( t \) in years. (Round \( k \) to \( 6 \) decimal places or enter an exact value for \( k \) .)

 b) What percentage of an original amount of Carbon- \( 14 \) is left after \( 15,000 \) years? (Round answer to the nearest tenth of a percent) 

c) If an old wooden tool found in a cave contains \( 58 \% \) of the original amount, approximately how old is the tool, within \( 10 \) years? 

Answer
expertExpert-Verified Answer

Fuentes Hilton
Qualified Tutor
4.0 (43votes)

a) 

\(\frac{1}{2}= e^{5730k}\Rightarrow  k= \frac{\ln \frac{1}{2} }{5730}\approx  - 0.000121\\\Rightarrow A(t)= Ne^{- 0.000121t}\)

 

c) 4500

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