3.Using the curve that you constructed for the decomposition of Carbon 14, find the age of a prehistoric cave painting discovered in the Lascaux Caves in southern France if the amount of Carbon 14 has decayed to 14.29%
To find the age of the prehistoric cave painting using the curve you constructed for the decomposition of Carbon 14, you would need to use the concept of half-life.
1. Determine the half-life of Carbon 14:
The half-life of Carbon 14 is approximately 5730 years. This means that after 5730 years, the amount of Carbon 14 in a sample will decrease by half.
2. Calculate the number of half-lives:
To find the number of half-lives, you can divide the natural logarithm of the remaining percentage of Carbon 14 (14.29%) by the natural logarithm of 0.5 (which represents the decrease by half in one half-life).
Number of half-lives = (ln (Remaining percentage of Carbon 14)) / (ln (0.5))
Number of half-lives = (ln (14.29)) / (ln (0.5))
3. Calculate the age of the cave painting:
The age can be calculated by multiplying the number of half-lives by the half-life of Carbon 14.
Age = Number of half-lives * Half-life of Carbon 14
By plugging in the values and performing the calculations, you can find the age of the prehistoric cave painting.