Question

the half - life of a particular radioactive substance is 3 months. if you started with 50 grams of this substance, how much of it would remain after 12 months? remaining amount = 50(1 - 0.50)^4 remaining amount = ? grams round your answer to the nearest whole number.

Explanation:

Step1: Calculate the exponent value

The half - life is 3 months and the time passed is 12 months. So the number of half - lives $n=\frac{12}{3}=4$.

Step2: Evaluate the expression

We have the formula for the remaining amount $A = 50(1 - 0.50)^4=50\times0.5^4$. First, calculate $0.5^4=0.5\times0.5\times0.5\times0.5 = 0.0625$. Then, $50\times0.0625 = 3.125$.

Step3: Round the result

Rounding 3.125 to the nearest whole number gives 3.

Answer:

3