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Algebra
Pregunta

A cave with beautiful prehistoric wall paintings w...

A cave with beautiful prehistoric wall paintings was discovered. Some charcoal found in the cave contained \( 27 \% \) of the \( { } ^ { 14 } C \)  expected in living trees. How old are the cave paintings? (The decay constant for \( { } ^ { 14 } C \) is 

Answer

A = current amount

\(A_0\)= original amount

\(0.27 A_0\) = A

\(A = A_0 e^{- 0.000121t}\)

\(\frac{A }{A_0} =  e^{- 0.000121t}\)

\(0.27 =  e^{- 0.000121t}\)

\(ln 0.27 = ln e^{- 0.000121t}\)

ln 0.27 = -0.000121t ln e

ln 0.27 = -0.000121t

-1.30933331998≈ -0.000121t

10820.9365288 ≈ t

Solución
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