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.
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: It represents the rate at which the amount of radioactive substance decreases each week. In this case, it is 1/2 or 50%.
w: It represents the number of weeks for which the substance has been decaying.
20: It represents the initial amount of the radioactive substance before any decay has occurred.
(1/2)^w: It represents the amount of radioactive substance remaining after w weeks, accounting for the rate of decay.
Autumn's Expression: (1−0.5)^w
w: It represents the number of weeks for which the substance has been decaying.
0.5: It represents the rate at which the amount of radioactive substance decreases each week. In this case, it is 0.5 or 50%.
1−0.5: It represents the remaining fraction of the radioactive substance after one week of decay, which is 0.5 or 50%.