Nick starts with 20
milligrams of a radioactive substance. The amount of the substance decreases by 12
each week for a number of weeks, w
. He writes the expression 20(12)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
CLEAR CHECK
Nick's Expression: 20(12)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(12)w
w: number of weeks
20: initial amount
(1/2)^w: decay factor after w weeks
12: percent decrease
1/2: decay factor for each week
Autumn's Expression: (1−0.5)^w
w: number of weeks
0.5: decay factor for each week
1−0.5: percent decrease