Grace starts with 100 milligrams of a radioactive substance. The amount of the substance decreases by 14
each week for a number of weeks, w. She writes the expression 100(14
)w to find the amount of radioactive substance remaining after w weeks.
Ryan starts with 1 milligram of a radioactive substance. The amount of the substance decreases by 40% each week for a number of weeks, w. He writes the expression (1 – 0.4)w to find the amount of radioactive substance remaining after w weeks.
Use the drop-down menus to explain what each part of Grace’s and Ryan’s expressions mean.
Grace’s Expression: 100(14
)w
100:
14
:
w:
(14
)w:
Ryan’s Expression: (1 – 0.4)w
1 – 0.4:
w:
0.4:
Grace’s Expression: 100(14)w
100: initial amount of radioactive substance in milligrams
14: amount the substance decreases each week in milligrams
w: number of weeks
(14)w: total decrease in milligrams after w weeks
Ryan’s Expression: (1 – 0.4)w
1 – 0.4: rate at which the substance decreases each week (60% remaining each week)
w: number of weeks
0.4: amount remaining after each week (40% of the original amount)