Eric starts with 10 milligrams of a radioactive substance. The amount of the substance decreases by 1/2 each week for a number of weeks, w. He writes the expression 10(1/2)ᵂ to find the amount of radioactive substance remaining after w weeks. Andrea starts with 1 milligram of a radioactive substance. The amount of the substance decreases by 20% each week for a number of weeks, w. She writes the expression (1 – 0.2)ᵂ to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Eric’s and Andrea’s expressions mean. Eric’s Expression: 10(1/2)ᵂ 1/2: w: 10: (1/2)ᵂ: Andrea’s Expression: (1 – 0.2)ᵂ.

Sure! Let’s break down both expressions used by Eric and Andrea.

Eric’s Expression: 10(1/2)ᵂ

1. 1/2: This represents the fraction of the radioactive substance that remains after each week. Since the amount halves, only 50% (or 1/2) of the substance stays each week.

2. w: This variable represents the number of weeks that have passed. It shows how many times the substance has halved.

3. 10: This is the initial amount of the radioactive substance Eric starts with, which is 10 milligrams.

4. (1/2)ᵂ: This part of the expression shows the process of halving the amount of the substance repeatedly for every week (w). The exponent w indicates that the halving occurs w times.

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Andrea’s Expression: (1 – 0.2)ᵂ

1. 0.2: This represents the decimal equivalent of the 20% decrease. It indicates that each week 20% of the substance is lost.

2. (1 – 0.2): This calculates the remaining percentage of the substance after the decrease, which is 80% (or 0.8). This shows what fraction of the substance remains each week.

3. w: Just like in Eric’s expression, this variable represents the number of weeks that have passed.

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