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=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.

Answer 1