Question

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.

Answer 1

Answer:

( 1  - 0.4)^w

Step-by-step explanation:

Grace starts with 100 milligrams of a radioactive substance. The amount of the substance decreases by 14 each week for a number of weeks

Amount remained after w weeks

= 100 - 14w

Ryan starts with 1 milligram of a radioactive substance. The amount of the substance decreases by 40% each week for a number of weeks

Amount remained after w weeks  

= 1 * (1  - 40/100)^w

= 1 * ( 1  - 0.4)^w

=

Answer 2

Answer: Grace ( 100: initial amount

1/4: decay factor for each week

w: number of weeks

(1/4)w: decay factor after w weeks)

Ryan ( 1-0.4: decay factor for each week

w: number of weeks

0.4: percent decrease)