Question

Cosmic ray bombardment of the atmosphere produces neutrons,
which in turn react with nitrogen to produce radioactive carbon-14.
Radioactive carbon-14 enters all living tissue through carbon
dioxide (via plants). As long as a plant or animal is alive,
carbon-14 is maintained in the organism at a constant level. Once
the organism dies, however, carbon-14 decays exponentially into
carbon-12. By comparing the amount of carbon-14 to the amount of
carbon-12, one can determine approximately how long ago the
organism died. (Willard Libby won a Nobel Prize for developing this
technique for use in dating archaeological specimens). The
half-life of carbon-14 is about 5730 years. In answering the
following questions, assume that the initial quantity of carbon-14
is 800 milligrams.

**a.** Construct an exponential function that
describles the relationship between A, the amount of carbon-14 in
milligrams, and t, the number of 5730-year time periods.

A(t)=

800e−0.000120968094*tEdit

**b.** Generate a table of values and plot the
function. Choose a reasonable set of values for the domain.
Remember that the objects we are dating may be up to 50,000 years
old.

Round your answers to two decimal places.

t | A |

0 | |

1 | |

2 | |

3 | |

4 | |

5 | |

6 | |

7 |

**c.** From your table, estimate how many milligrams
are left after 25,000 years and after 45,000 years.

Round your answers to two decimal places.

A≈ milligrams when the number of years is 25,000.

A≈ milligrams when the number of years is 45,000.

**d.** Now construct an exponential function that
describes the relationship between A and T, where T is measured in
years. What is the annual decay factor? The annual decay
rate?

Round a to six decimal places.

The exponential function is A=CaT, where C= and a≈

**e.** Use your function in part **(d)**
to calculate the number of milligrams that would be left after
25,000 years and after 45,000 years.

Round your answers to three decimal places.

A≈ milligrams when the number of years is 25,000.

A≈ milligrams when the number of years is 45,000.

Answer #1

The radioactive isotope 14C is produced in the earth’s
atmosphere by bombardment of nitrogen by cosmic rays. The 14C
enters living organisms, where the ratio of 14C to 12C is the same
as in the atmosphere, about . After 1.20×10―12an organism dies, the
14C decays with a half-life of 5730 years. The mass of a neutral
12C atom is 1.993kg.×10―26
(a) A tapestry is determined by mas spectroscopy to contain a
ratio of 14C to 12C of . How old...

Carbon 14 is a radioactive isotope of carbon, the most common
isotope of carbon being carbon 12. Carbon 14 is created when cosmic
ray bombardment changes nitrogen 14 to carbon 14 in the upper
atmosphere. The resulting carbon 14 combines with atmospheric
oxygen to form radioactive carbon dioxide, which is incorporated
into plants by photosynthesis. Animals acquire carbon 14 by eating
plants. When an animal or plant dies, it ceases to take on carbon
14, and the amount of isotope...

please do this step by step and in detail please!!!
extremely stuck on this problem and i just don't get it
help!
30. Radiocarbon Dating.
Carbon 14 is a radioactive isotope of carbon, the most common
isotope of carbon being carbon 12. Carbon 14 is created when cosmic
ray bombardment changes nitrogen 14 to carbon 14 in the upper
atmosphere. The resulting carbon 14 combines with atmospheric
oxygen to form radioactive carbon dioxide, which is incorporated
into plants by photosynthesis....

(A)This exercise uses the radioactive decay model.
The burial cloth of an Egyptian mummy is estimated to contain 58%
of the carbon-14 it contained originally. How long ago was the
mummy buried? (The half-life of carbon-14 is 5730 years. Round your
answer to the nearest ten years.)
yr
(b)This exercise uses the radioactive decay model.
A wooden artifact from an ancient tomb contains 60% of the
carbon-14 that is present in living trees. How long ago was the
artifact made?...

The exponential decay function for 80 mg of the radioactive
isotope nitrogen-12 is given by the function below, where t is in
minutes:
y(t)=80e-0.0696t
Find the rate of change of the radioactive isotope after 22
minutes has elapsed. Round answer to 2 decimal
places.
SHOW WORK

Q1. Carbon-14 – or 14C – is a radioactive isotope of carbon with
a half-life of 5,730 years. It decays into nitrogen-14 – or 14N – ,
which is a stable isotope of nitrogen.
(a) Which of the three nuclear decay processes describes the decay?
Explain. (Hint: You can get the atomic number of carbon and
nitrogen from a periodic table.)
(b) Write down the equation for the decay.
(c) What is the decay constant for 14C?
All isotopes of...

An exponential decay function can be used to model the number of
grams of a radioactive material that remain after a period of
time. Carbon-14 decays over time, with the amount remaining after
t years given by y=y 0 e Superscript negative 0.00012378
ty=y0e−0.00012378t, where y0 is the original amount. If the
original amount of carbon-14 is 450450 grams, find the number of
years until 346346 grams of carbon-14 remain.

Background:
Excavations at Stonehenge uncovered a number of unshed antlers,
antler tines, and animal bones. Carbon-14 dating methods were used
to estimate the ages of the Stonehenge artifacts. Carbon-14 is one
of three carbon isotopes found in Earth’s atmosphere. Carbon-12
makes up 99% of all of the carbon dioxide in the air. Virtually all
of the remaining 1% is composed of carbon-13. By far, the rarest
form of carbon isotope found in the atmosphere is carbon-14.
The ratio of carbon-14...

Background:
Excavations at Stonehenge uncovered a number of unshed antlers,
antler tines, and animal bones. Carbon-14 dating methods were used
to estimate the ages of the Stonehenge artifacts. Carbon-14 is one
of three carbon isotopes found in Earth’s atmosphere. Carbon-12
makes up 99% of all of the carbon dioxide in the air. Virtually all
of the remaining 1% is composed of carbon-13. By far, the rarest
form of carbon isotope found in the atmosphere is carbon-14.
The ratio of carbon-14...

Carbon Dating: All living organisms contain two isotopes (types)
of carbon; carbon-12 ( 12C) and carbon-14 (14C). Carbon-12 is
stable, meaning that its atoms do not decay. Carbon-14 however, is
radioactive or unstable, meaning that an atom of carbon-14 may
decay. It does this by throwing off an electron and thus
transforming itself into Nitrogen 14. The ratio of carbon-14 to
carbon-12 is the same for all living organisims, about 1/10, 000.
However, once an organisim dies the carbon-14 begins...

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