Question

the half - life of a particular radioactive substance is 3 years. if you started with 60 grams of this substance, how much of it would remain after 6 years? remaining amount = ?(1 - )^ remaining amount = i(1 - r)^t enter the number that belongs in the green box.

Explanation:

Step1: Identify the initial amount

The initial amount $I$ of the radioactive substance is 60 grams. This is the value that goes in the green - box in the formula $Remaining\ Amount = I(1 - r)^t$.

Step2: Determine the decay rate

The half - life is 3 years. In 3 years, half of the substance decays. So the decay rate $r=\frac{1}{2}$.

Step3: Calculate the number of half - lives

The time $t = 6$ years and the half - life is 3 years. The number of half - lives $n=\frac{6}{3}=2$.

Step4: Use the decay formula

Substitute $I = 60$, $r=\frac{1}{2}$ and $t = 2$ into the formula $Remaining\ Amount=I(1 - r)^t$. First, $1-r=1-\frac{1}{2}=\frac{1}{2}$, and $(1 - r)^t=(\frac{1}{2})^2=\frac{1}{4}$. Then $Remaining\ Amount = 60\times\frac{1}{4}=15$ grams. But we are only asked for the value in the green box which is the initial amount.

Answer:

60