Question in picture about calculus. Thanks! 1. (Based on 7.6.33. from the book) The method of carbon dating makes use of thefact that all living organisms contain two isotopes of carbon, carbon-12, denoted12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope). Theratio of the amount of 14C to the amount of 12C is essentially constant in a livingorganism (approximately 1 to 1 trillion). When an organism dies, the amountof 12C present remains unchanged, but the 14C decays at a rate proportional tothe amount present with a half-life of approximately 5700 years. This change inthe amount of 14C relative to the amount of 12C makes it possible to estimatethe time at which the organism lived.Let A, be the amount of 14C present in some living organism just(a)before it dies. Write an equation for A(t), the amount of 14C present in adead organism t years after it dies.(b)Suppose that for some fossil found in an archaeological dig the ratioof the amount of 14C to the amount of 12C of is approximately 1 to 5trillion. What is the approximate age of the fossil?Let Rx 10-12 be the approximate ratio of the amount of 14C to the(c)amount of 12C measured in some fossil (so R = 0.2 in (b)). Show thatamount, A(t), of 14C present in this fossil is A, · R. Hint: explain whyoriginal amount of 14C10-12A(t)current amount of 14CR× 10-12*(d)Conclude that the age of this fossil ist = -5700 In(R)/In(2).yеars.

For living organisms; C14C12 = constant = 11012 Hence, 14C just before the organism dies; C14 =C12…

1. (Based on 7.6.33. from the book) The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope). The ratio of the amount of 14C to the amount of 12C is essentially constant in a living organism (approximately 1 to 1 trillion). When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years. This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived. (a) Let Ao be the amount of 14C present in some living organism just

1. (Based on 7.6.33. from the book) The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope). The ratio of the amount of 14C to the amount of 12C is essentially constant in a living organism (approximately 1 to 1 trillion). When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years. This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived. (a) Let Ao be the amount of 14C present in some living organism just

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question in picture about calculus. Thanks!

1. (Based on 7.6.33. from the book) The method of carbon dating makes use of the
fact that all living organisms contain two isotopes of carbon, carbon-12, denoted
12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope). The
ratio of the amount of 14C to the amount of 12C is essentially constant in a living
organism (approximately 1 to 1 trillion). When an organism dies, the amount
of 12C present remains unchanged, but the 14C decays at a rate proportional to
the amount present with a half-life of approximately 5700 years. This change in
the amount of 14C relative to the amount of 12C makes it possible to estimate
the time at which the organism lived.
Let A, be the amount of 14C present in some living organism just
(a)
before it dies. Write an equation for A(t), the amount of 14C present in a
dead organism t years after it dies.
(b)
Suppose that for some fossil found in an archaeological dig the ratio
of the amount of 14C to the amount of 12C of is approximately 1 to 5
trillion. What is the approximate age of the fossil?
Let Rx 10-12 be the approximate ratio of the amount of 14C to the
(c)
amount of 12C measured in some fossil (so R = 0.2 in (b)). Show that
amount, A(t), of 14C present in this fossil is A, · R. Hint: explain why
original amount of 14C
10-12
A(t)
current amount of 14C
R× 10-12*
(d)
Conclude that the age of this fossil is
t = -5700 In(R)/In(2).
yеars.

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