Nick starts with 20
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 20(1/2)^w
to find the amount of radioactive substance remaining after w
weeks.
Autumn starts with 1
milligram of a radioactive substance. The amount of the substance decreases by 50%
each week for a number of weeks, w
. She writes the expression (1−0.5)^w
to find the amount of radioactive substance remaining after w
weeks.
Use the drop-down menus to explain what each part of Nick's and Autumn's expressions mean.
number of weeks
initial amount
decay factor after w weeks
percent decrease
decay factor for each week
Nick's Expression: 20(1/2)^w
1/2:
w:
20:
(1/2)^w:
Autumn's Expression: (1−0.5)^w
w:
0.5:
1−0.5:
Nick's Expression: 20(1/2)^w
1/2: The decay factor for each week, indicating that the amount of substance decreases by half every week.
w: The number of weeks over which the substance is decaying.
20: The initial amount of radioactive substance.
(1/2)^w: The decay factor after w weeks, indicating how much of the substance remains after w weeks.
Autumn's Expression: (1−0.5)^w
w: The number of weeks over which the substance is decaying.
0.5: The decay factor for each week, indicating that the amount of substance decreases by 50% every week.
1−0.5: The percent decrease, indicating that 50% of the substance is decaying every week.