Math  /  Algebra

QuestionThe amount of carbon 14 remaining in a sample that originally contained AA grams is given by C(t)=A(0.999879)tC(t)=A(0.999879)^{t} where tt is time in years. How old, to the nearest 1,000 years, is a fossil in which only 33%33 \% of the carbon 14 has decayed? \square yr

Studdy Solution
Calculate the value of t t and round to the nearest 1,000 years:
Calculate:
tln(0.67)ln(0.999879) t \approx \frac{\ln(0.67)}{\ln(0.999879)}
Using a calculator:
t0.40047756660.0001210005 t \approx \frac{-0.4004775666}{-0.0001210005} t3309.7 t \approx 3309.7
Round to the nearest 1,000 years:
t3,000 years t \approx 3,000 \text{ years}
The age of the fossil is approximately:
3,000 years \boxed{3,000} \text{ years}

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