Which of the following situations represents a linear relationship? a. a radioactive substance loses half of its mass every 12 years. b. the volume of a cubical gift box depends on the side length of the box. c. the cost of living increases in a certain area by 3 percent each year. d. susie is losing 5 pounds every month on her diet.

A. A radioactive substance loses half of its mass every 12 years.

Half of mass loses every 12 years. So there is no common difference. Its an exponential relationship.

B. The volume of a cubical gift box depends on the side length of the box.

The volume of the box depends on the length , width and height of the box.

It does not depends on single side. So its not a linear .

C. The cost of living increases in a certain area by 3 percent each year

The cost of living increases by 3%. So there is no constant change every year.Hence it is not a linear

D. Susie is losing 5 pounds every month on her diet.

Susie losing 5 pounds every month. that is constant for every month. Rate of change is constant so it is a linear relationship.

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