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Statistics: Informed Decisions Using Data | 4th Edition | ISBN: 9780321757272 | Authors: Michael Sullivan, III
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Chemistry A chemist has a 100-gram sample of a radioactive

Chapter 4, Problem 38E

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QUESTION:

Problem 38E

Chemistry A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material in the sample every week for 6 weeks and obtains the following data. Theory states that the amount of radioactive material will decline according to the law of uninhibited decay. This law states that the amount of radioactive material in the sample will decline exponentially over time.

Week, x

Weight (grams), y

Week, x

Weight (grams), y

0

100.0

4

59.1

1

88.3

5

51.8

2

75.9

6

45.5

3

69.4

 

 

(a) Draw a scatter diagram treating time as the explanatory variable.

(b) Determine the logarithm of the y-values so that Y = log y.Draw a scatter diagram of the transformed data.

(c) Find the least-squares regression line of the transformed data.

(d) Find the exponential equation of best fit.

(e) Use the exponential equation of best fit to predict the amountof radioactive material after 10 weeks.

Questions & Answers

QUESTION:

Problem 38E

Chemistry A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material in the sample every week for 6 weeks and obtains the following data. Theory states that the amount of radioactive material will decline according to the law of uninhibited decay. This law states that the amount of radioactive material in the sample will decline exponentially over time.

Week, x

Weight (grams), y

Week, x

Weight (grams), y

0

100.0

4

59.1

1

88.3

5

51.8

2

75.9

6

45.5

3

69.4

 

 

(a) Draw a scatter diagram treating time as the explanatory variable.

(b) Determine the logarithm of the y-values so that Y = log y.Draw a scatter diagram of the transformed data.

(c) Find the least-squares regression line of the transformed data.

(d) Find the exponential equation of best fit.

(e) Use the exponential equation of best fit to predict the amountof radioactive material after 10 weeks.

ANSWER:

Answer

Step 1 of 5

(a)

A chemist records the amount of radioactive material in the sample every week for 6 weeks and obtains the following data.

Week, x

Weight (grams), y

Week, x

Weight (grams), y

0

100.0

4

59.1

1

88.3

5

51.8

2

75.9

6

45.5

3

69.4

 

 

 

We are asked to draw a scatter diagram treating time as the explanatory variable.

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