Question

the half - life of a particular radioactive substance is 1 year. if you started with 40 grams of this substance, how much of it would remain after 3 years? remaining amount =? (1 - ) remaining amount = i(1 - r)^t enter the number that belongs in the green box.

Explanation:

Step1: Identify the decay formula parameters

The half - life formula for radioactive decay is $A = I(1 - r)^t$, where $I$ is the initial amount, $r$ is the decay rate, and $t$ is the time. For a half - life problem, if the half - life is $h$, then $r=\frac{1}{2}$ when $t = h$. Here, $h = 1$ year, $I=40$ grams, and $t = 3$ years.

Step2: Substitute values into the formula

Substitute $I = 40$, $r=\frac{1}{2}$, and $t = 3$ into $A = I(1 - r)^t$. We get $A=40\times(1-\frac{1}{2})^3$.

Step3: Calculate the remaining amount

First, calculate $(1-\frac{1}{2})^3=(\frac{1}{2})^3=\frac{1}{8}$. Then, $A = 40\times\frac{1}{8}=5$ grams.

Answer:

5