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
12:
w:
20:
(12)w:
Autumn's Expression: (1−0.5)w
w:
0.5:
1−0.5:
Nick's Expression:
12: This represents the amount that the substance decreases by each week.
w: This represents the number of weeks.
20: This represents the initial amount of the substance.
(12)w: This represents the total decrease in the substance after w weeks.
Autumn's Expression:
w: This represents the number of weeks.
0.5: This represents the decay factor for each week, which is a 50% decrease.
1−0.5: This represents the remaining amount after each week's decrease.