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) = A₀e^kt.

(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?