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 each expression step by step.
Eric’s Expression: 10(1/2)^w
1. 1/2: This represents the proportion of the substance that remains each week. Each week, half of the substance is lost, meaning 50% remains.
2. w: This stands for the number of weeks that have passed. It is the variable indicating how long the substance has been decreasing.
3. 10: This is the initial amount of the radioactive substance that Eric starts with, which is 10 milligrams.
4. (1/2)^w: This part of the expression calculates the fraction of the original substance remaining after w weeks. It represents how the amount of substance decreases over time.
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Andrea’s Expression: (1 – 0.2)^w
– (1 – 0.2): This represents the amount of the substance that remains after losing 20%. Since 20% is lost, 80% (or 1 – 0.2) remains.
– w: This is the same as in Eric’s expression; it indicates the number of weeks that have passed.
Overall, both expressions illustrate exponential decay over time, but with different rates and initial quantities. If you have any more questions, feel free to ask!