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Radioisotope Dating
Exponential decay occurs with radioactive substances. This fact can help scientists estimate the age of objects. All living creatures contain carbon. Some of that carbon is in the form of radioactive Carbon-14. Since it is radioactive, carbon-14 decays. This substance decays fairly slowly; it decreases by approximately 1.202% every 100 years. If an archeologist unearthed a fossil of a once living creature, the amount of carbon-14 remaining in that fossil would help the archeologist calculate the number of years since the creature died. This is called carbon dating.
If a fossil contained 75% of the original carbon-14, how old is the fossil?
Solving with Logarithms
To get a more exact answer to the question above, you can use the equation of the function and solve for time. Start with the equation: y = 100 * (1-.01202)x where, y is the percent of carbon-14 remaining in the fossil and x is the number of 100 year increments that have passed since the creature died.
Plug in 75 for y: 75 = 100 * (1-.01202)x
Solve using logarithms:
Since x is the number of 100 year increments, we need to multiply the answer by 100 to get the number of years since the creature died.
