Question

A has a half life of 5 years. Find the amount of life left after 15 years.

• A. $\frac{1}{8}$ of initial value
• B. $\frac{7}{8}$ of initial value
• C. $\frac{1}{4}$ of initial value
• D. $\frac{3}{4}$ of initial value

Answer 1

Answer: (A)

$\frac{1}{8}$ of initial value

Answer 2

If the half-life of substance A is 5 years, then after 5 years, the amount of substance A remaining will be half of its initial amount.
After another 5 years (i.e. 10 years in total), the amount of substance A remaining will be half of the amount remaining after 5 years, or one quarter of the initial amount.
After another 5 years (i.e. 15 years in total), the amount of substance A remaining will be half of the amount remaining after 10 years, or one eighth of the initial amount.
Therefore, the answer is $\frac{1}{8}$ of the initial value.
So, the correct answer is (A) : $\frac{1}{8}$ of initial value.