Question

Eric starts with 10 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 10(12)w to find the amount of radioactive substance remaining after w weeks. Andrea starts with 1 milligram of a radioactive substance. The amount of the substance decreases by 20% each week for a number of weeks, w. She writes the expression (1−0.2)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Eric’s and Andrea’s expressions mean.

Answer 1

Andrea's Expression: (1 - 0.2)^w

w: number of weeks

0.2: percent decrease

1 - 0.2: decay factor for each week

I got Eric's Expression wrong :(

Answer 2

Answer and explanation:

Eric's expression is $10(\frac{1}{2})^w$ and Andrea's is $(1-0.2)^w$.

In Eric's expression, 10 represents the amount of substance he begins with.  1/2 is the amount of substance left after each time period (in this case, each week).

Andrea's expression can be written as $1(1-0.2)^w$.  The one outside of parentheses represents the initial amount of the substance.  The one inside of parentheses represents 100% of the original amount of the substance.  0.2 represents the 20% of the substance that is lost each time period.  The variable w in this case represents the number of weeks.