Question

the half - life of a particular radioactive substance is 1 week. if you started with 70 grams of this substance, how much of it would remain after 3 weeks? remaining amount = 70(1 - 0.50)^t remaining amount = i(1 - r)^t enter the number that belongs in the green box.

Explanation:

Step1: Identify the decay formula variables

The half - life formula for radioactive decay is $A = A_0(1 - r)^t$, where $A_0$ is the initial amount, $r$ is the decay rate, and $t$ is the time. Given half - life $T = 1$ week, the decay rate $r=0.5$ (since half of the substance decays each week), $A_0 = 70$ grams, and $t = 3$ weeks.

Step2: Substitute values into the formula

Substitute $A_0 = 70$, $r = 0.5$, and $t = 3$ into the formula $A=A_0(1 - r)^t$. We get $A = 70\times(1 - 0.5)^3$.

Step3: Calculate the result

First, calculate $(1 - 0.5)^3=(0.5)^3=0.125$. Then, $A = 70\times0.125 = 8.75$ grams.

Answer:

8.75