Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.

D

Step-by-step explanation:

Option D - It is the product of the initial amount and the decay factor after w weeks.

Step-by-step explanation:

Given : Ariana starts with 100 milligrams of a radioactive substance. The amount of the substance decreases by 20% each week for a number of weeks, w. The expression finds the amount of radioactive substance remaining after w weeks.

To find : Which statement about this expression is true?

Solution :

In Ariana's expression,  

100 represents the amount of substance he begins with.

and (1-0.2) i.e, 0.8 is the amount of substance left after each time period or the decay factor after w weeks.  

The given expression represents the product of initial amount and the decay factor after w weeks.

Therefore, Option D is correct.

  D.  It is the product of the initial amount and the decay factor after w weeks.

Step-by-step explanation:

We are told that Ariana starts with 100 milligrams of the substance. The number 100 in the expression likely represents this amount, the initial amount. It is multiplied by another number, so is part of a product. (It is not part of a difference, and is not something that is raised to a power.)

The factor (1 -0.2) represents the fraction remaining at the end of a week. That number raised to the power w will represent the fraction remaining at the end of w weeks. This fraction can reasonably be referred to as "the decay factor after w weeks."

Hence, the expression represents ...

  the product of the initial amount and the decay factor after w weeks