A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material
Question:
A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 7 weeks and obtains the following data:
Week ………………………………. Weight (in Grams)
0 …………………………………………….…. 69.4
1 ……………………………………………… 100.0
2 ……………………………………………….. 88.3
3 ……………………………………………….. 75.9
4 ……………………………………………….. 59.1
5 ……………………………………………….. 51.8
6 ……………………………………………….. 45.5
(a) Using a graphing utility, draw a scatter diagram with week as the independent variable.
(b) Using a graphing utility, build an exponential model from the data.
(c) Express the function found in part (b) in the form A(t) = A0ekt.
(d) Graph the exponential function found in part (b) or (c) on the scatter diagram.
(e) From the result found in part (b), determine the half-life of the radioactive material.
(f) How much radioactive material will be left after 50 weeks?
(g) When will there be 20 grams of radioactive material?
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