Question

the half - life of a particular radioactive substance is 1 week. if you started with 80 grams of this substance, how much of it would remain after 3 weeks? remaining amount = (1 - 1/2)^t remaining amount = (1 - 1/2)^3 enter the number that belongs to the green box.

Explanation:

Step1: Identify decay formula

The formula for radioactive - decay is $A = A_0(\frac{1}{2})^{\frac{t}{T}}$, where $A$ is the remaining amount, $A_0$ is the initial amount, $t$ is the time elapsed, and $T$ is the half - life. Here, $A_0 = 70$ grams, $t = 3$ weeks, and $T = 1$ week.

Step2: Substitute values into formula

Substitute the values into the formula: $A=70\times(\frac{1}{2})^{\frac{3}{1}}$.

Step3: Calculate the result

First, calculate $(\frac{1}{2})^3=\frac{1}{8}$. Then, $A = 70\times\frac{1}{8}=\frac{70}{8}=8.75$ grams.

Answer:

$8.75$ grams