Question

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.

Answer 1

D

Explanation:

Answer 2

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

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
`100(1-0.2)^w` 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(1-0.2)^w`

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.