Prehistoric cave paintings were discovered in a cave in France. The paint contained 10 %10% of the original​ carbon-14. Use the exponential decay model for​ carbon-14, Upper A equals Upper A 0 e Superscript negative 0.000121 t=A0e−0.000121t​, to estimate the age of the paintings.

Accepted Solution

Answer: t=19188.2 yStep-by-step explanation:The exponential decay equation is:[tex] A=A_{0}e^{-0.00012t}[/tex]      (1)But, A is 10% of A₀, it means that A=0.10A₀.If we put it into equation (1), we will have:[tex] 0.10A_{0}=A_{0}e^{-0.00012t}[/tex]      [tex] 0.10=e^{-0.00012t}[/tex]         (2)Now, we just need to solve (2) for t.[tex] t=\frac{ln(0.10)}{-0.000121} = 19188.2 y [/tex]      I hope it helps you!