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 initial amount raised to the decay factor after w weeks.
It is the difference between the initial amount and the decay factor after w weeks.
It is the product of the initial amount and the decay factor after w weeks.
The correct answer is: It is the product of the initial amount and the decay factor after w weeks.
Explanation: The expression (100(1 – 0.2)^{w}) simplifies to (100(0.8)^{w}). Here, 100 represents the initial amount of the substance, and (0.8) represents the decay factor (which is 1 minus the percentage decrease of 20%). The expression calculates the remaining amount of the substance after (w) weeks by multiplying the initial amount by the decay factor raised to the power of (w).