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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Dinosaur fossils are often dated by using an element other than carbon, such as potassium-40, that has a longer half-life (in this case, approximately 1.25 billion years). Suppose the minimum detectable amount is 0.1% and a dinosaur is dated with 40K 10 be 68 million years old. Is such a dating possible? In other words, what is the maximum age of a fossil that we could date using 40K?

To determine

To find: The maximum age of the fossil using potassium-40.

Explanation

Given:

The half-life of potassium-40 is 1.25 billion years. That is, A(t)=0.5A0 where t=1.25×109 years.

Minimum detectable amount is 0.1% of the initial amount A(t)=0.001A0.

Calculation:

Consider the exponential model is A(t)=A0ekt (1)

Substitute A(1.25×109)=0.5A0 in equation (1),

0.5A0=A0e1.25×109k0.5=e1.25×109k

Take natural logarithm on both sides,

ln0.5=lne1.25×109kln0.5=1.25×109k   (Qlnem=m)k=ln0.51.25×109k=0.5545109

That is, k=0

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