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
Let’s break down each part of Eric’s and Andrea’s expressions:
Eric’s Expression: 10(1/2)^w
– 1/2: This represents the fraction by which the substance decreases each week. It signifies that each week, the amount of substance is halved.
– w: This stands for the number of weeks that have passed. It is the variable that changes based on how long the substance has been decaying.
– 10: This is the initial amount of the radioactive substance Eric starts with, which is 10 milligrams.
– (1/2)^w: This part of the expression calculates the proportion of the original amount remaining after w weeks due to the halving effect each week.
Andrea’s Expression: (1 – 0.2)^w
– 0.2: This represents the percentage decrease in the amount of substance each week, which is 20%.
– w: This also stands for the number of weeks that have passed, similar to Eric’s expression.
– (1 – 0.2): This calculates the remaining percentage of the substance after one week, which is 80% or 0.8 of the substance.
In summary, Eric’s formula shows half-life decay weekly for a larger initial quantity, while Andrea’s formula models a percentage decay for a smaller initial amount. If you have more questions or need further assistance, feel free to ask!