Question

Cosmic ray bombardment of the atmosphere produces neutrons, which in turn react with nitrogen to produce...

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=C⁢aT, 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.

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