(a) 500(1/2)^t
(b.1) 500(1/2)^(25000/5730)
= 500(1/2)^4.363 = 24.3
see what you can do from here.
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 500 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.
b. From your table, estimate how many milligrams are left after 25,000 years and after 40,000 years.
Round your answers to two decimal places.
_________milligrams when the number of years is 25,000
_________milligrams when the number of years is 40,000
c.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=Ca^T where C=____ and A=____
d. Use your function in part (d) to calculate the number of milligrams that would be left after 25,000 years and after 40,000 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 40,000
1 answer
1 answer