Question

Some cave paintings were discovered today in a cave in Spain. The paint contained 34% of the original carbon-14. Estimate the age of the paintings using the exponential decay model for carbon-14, A=A0e^-0.000121t (round to the nearest whole number as needed.) The paintings are approximately ? years old.

Answer 1

Answer:

The age of the painting is 8916 years

Solution:

As per the question:

Exponential decay is given as:

$A = A_{o}e^{- 0.000121t}$

where

A = amount of carbon left after 't' years

$A_{o}$ = Initial amount of the carbon

Also,

A = 34%$A_{o} = 0.34A_{o}$

To calculate the how much older the painting is put $A = 0.34A_{o}$ in the given equation for the exponential decay as:

$0.34A_{o} = A_{o}e^{- 0.000121t}$

$0.34 = e^{- 0.000121t}$

Take natural log on both sides of the equation:

$ln{0.34} = ln{e^{- 0.000121t}}$

$- 1.0788 = - 0.000121t$

t = 8915.78 years ≈ 8916 years