ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20%…

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? it is the difference between the initial amount and the percent decrease. it is the difference between the initial amount and the decay factor after w weeks. it is the initial amount raised to the decay factor after w weeks. it is the product of the initial amount and the decay factor after w weeks.

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? it is the difference between the initial amount and the percent decrease. it is the difference between the initial amount and the decay factor after w weeks. it is the initial amount raised to the decay factor after w weeks. it is the product of the initial amount and the decay factor after w weeks.

Answer

Answer:

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

Explanation:

Step1: Identify the decay - formula

The general formula for exponential decay is $A = A_0(1 - r)^w$, where $A_0$ is the initial amount, $r$ is the rate of decay, and $w$ is the number of time - periods. Here, $A_0 = 100$, $r=0.2$, and the amount of radioactive substance remaining $A = 100(1 - 0.2)^w=100\times0.8^w$. The expression $100(1 - 0.2)^w$ is the product of the initial amount $A_0 = 100$ and the decay factor $(1 - 0.2)^w$ after $w$ weeks.