Question

the half - life of a particular radioactive substance is 1 year. if you started with 50 grams of this substance, how much of it would remain after 3 years? remaining amount = ?(1 - )^ remaining amount = i(1 - r)^t

Explanation:

Step1: Identify initial amount

The initial amount $I = 50$ grams.

Step2: Identify decay rate

Since the half - life is 1 year, the decay rate $r=\frac{1}{2}$.

Step3: Identify time

The time $t = 3$ years.

Step4: Calculate remaining amount

Substitute $I = 50$, $r=\frac{1}{2}$, and $t = 3$ into the formula $Remaining\ Amount=I(1 - r)^t$. So, $Remaining\ Amount=50\times(1-\frac{1}{2})^3=50\times(\frac{1}{2})^3=50\times\frac{1}{8}=\frac{50}{8} = 6.25$ grams.

Answer:

$6.25$ grams