In the year 2005, a picture supposedly painted by a famous artist sometime after 1655 but before 1705 contains 98.3 percent of its carbon-14 (half-life 5730 years). Approximately how old is the painting in years?

The age of the painting can be calculated using the concept of carbon-14 dating. Carbon-14 is an isotope that decays over time, with a half-life of 5730 years.

In the year 2005, the painting contained 98.3 percent of its carbon-14, indicating that approximately 1.7 percent of the carbon-14 has decayed.

By finding the amount of time it takes for 1.7 percent of the carbon-14 to decay, we can determine the age of the painting.

First, we need to find the ratio of the remaining carbon-14 to the original amount. If 98.3 percent of the carbon-14 remains, then 1.7 percent has decayed.

Since the half-life of carbon-14 is 5730 years, we can calculate the time it takes for 1.7 percent to decay by dividing 5730 by 100 and multiplying by 1.7.

This gives us 97.41 years.

To calculate the approximate age of the painting, we subtract 97.41 years from the year 2005:

2005 - 97.41 = 1907.59

Therefore, the painting is approximately 1908 years old.

Learn more about carbon-14 dating here:

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