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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Dinosaur fossils are too old to be reliably dated using carbon-14. (See Exercise 11.) Suppose we had a 68-millionyear-old dinosaur fossil. What fraction of the living dinosaur's 14C would be remaining today? Suppose the minimum detectable amount is 0.1 %. What is the maximum age of a fossil that we could date using 14C?

To determine

To find: The fraction of the living dinosaur’s C14 would be remaining today and maximum age of the fossil C14.

Explanation

Given:

The half-life of C14 is 5730 years. That is, A(5730)=0.5A0.

Calculation:

The exponential model is A(t)=A0ekt (1)

Substitute A(5730)=0.5A0 in equation (1),

0.5A0=A0e5730k0.5=e5730k

Take natural logarithm on both sides,

ln0.001=lne5730kln0.5=5730k   (Qlnem=m)k=ln0.55730

Substitute k=ln0.55730 in equation (1),

A(t)=A0eln0.55730t (2)

Substitute 68,000,000 for t in equation (2),

A(68,000,000)=A0eln0

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