Maths problem[Estimation]

hoi wing

2009-07-09 1:06 am

By measuring the radioactivity(P%) of the carbon-14 element that an ancient specimen contains, we can estimate the specimen's age(t). The relationship between P and t is as follows:

P= 100(0.5)^t/5760

Using the eqt. above, estimate the age of the following specimens.
(a) A fossil from the end of the last ice age, for which the measured value of P is 22. [Ans: 12580]
(b) The wood in a tomb, for which the measured value of P is 68.9. [Ans: 3096]
(Give the ans. cor. to 4 sig. fig.)

Can anyone calculate them in details? thx!

回答 (2)

用戶9112

2009-07-09 2:11 am

✔ 最佳答案

P= 100(0.5)t/5760

(a) P = 22 = 100(0.5)t/5760
(0.5)t/5760 = 0.22
(t/5760)log(0.5) = log(0.22)
t/5760 = log(0.22)/log(0.5) = 2.1844
t = 12,580 years
(b) P = 68.9 = 100(0.5)t/5760
(0.5)t/5760 = 0.689
(t/5760)log(0.5) = log(0.689)
t/5760 = log(0.689)/log(0.5) = 0.53742
t = 3,096 years

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hoi wing

2009-07-09 3:25 am

thx so much!

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