Question

Nick starts with 20 milligrams of a radioactive substance. The amount of the substance decreases by 14 each week for a number of weeks, w. He writes the expression 20(14)w to find the amount of radioactive substance remaining after w weeks. Autumn starts with 5 milligrams 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.

Answer 1

Answer:

Eric's expression is :

$20(\frac{1}{4})^w$

and Andrea's is :

$(1-0.5)^w$

In Eric's expression, 20 represents the initial amount of substance with which he has started the experiment. $\thinspace \frac{1}{4}\thinspace$ is the amount of substance left after each time period (in this case, each week).The variable w in this case represents the number of weeks.

Andrea's expression can be written as :

$1\cdot (1-0.5)^w$

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. 0.5 represents the 50% of the substance that is lost each time period. The variable w in this case represents the number of weeks.

Answer 2

Answer:

Step-by-step explanation:

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.

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: