SOLUTION: In 1964, paleontologists discovered the bones of a new species of dinosaur. The age of the dinosaur was estimated using potassium-40 dating of rocks surrounding the bones. Analysis

Question 321314: In 1964, paleontologists discovered the bones of a new species of dinosaur. The age of the dinosaur was estimated using potassium-40 dating of rocks surrounding the bones. Analysis of these rocks indicated that 82.8% of the original amount of the potassium-40 was still present. The decay model for potassium-40 is A=A(subzero)e^(-0.52912t), where t is in billions of years. Let A=0.828A(subzero) in this decay model and estimate the age of the bones of the dinosaur. The bones are _ billion years old. Round to four decimal places as needed.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Analysis of these rocks indicated that 82.8% of the original amount of the potassium-40 was still present.
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The decay model for potassium-40 is A=A(subzero)e^(-0.52912t), where t is in billions of years. Let A=0.828A(subzero) in this decay model and estimate the age of the bones of the dinosaur. The bones are _ billion years old. Round to four decimal places as needed.
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A(t) = Ao*e^(-0.52912t)
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0.828*A0 = Ao*e^(-0.52912t)
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e^(-0.52912t) = 0.828
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Take the natural log to get:
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-0.52912t = -0.1887
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t = 0.3567 billion years old
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Cheers,
Stan H.
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