# Which graph is the correct answer?

## The weight of a radioactive isotope was 96 grams at the start of an experiment. After one hour, the weight of the isotope was half of its initial weight. After two hours, the weight of the isotope was half of its weight the previous hour. If this pattern continues, which of the following graphs represents the weight of the radioactive isotope over time? Graph W Graph X Graph Y Graph Z

Jun 26, 2018

Graph W

#### Explanation:

Graph Y and Z are easily ruled out as they start at $120 g$ at 0 hours, however, our substance starts at $96 g$ at 0 hours.

This leaves Graph W and Graph X. We know that at hour 1 our substance is half the mass of hour 0. We know it started at $96 g$ at hour 0 therefore hour 1's mass must be$\frac{1}{2} \cdot 96 g = 48 g$

Graph W has $48 g$ left at Hour 1 while Graph X has $24 g$ this means Graph W must be our correct graph.

Jun 26, 2018

Graph W.

#### Explanation:

Graphs Y and Z do not start at the correct initial value. Graph X shows a $\frac{1}{4}$ level after 2 hours instead of $\frac{1}{2}$ and follows a half-life of $\frac{1}{2}$ Hour instead of one hour. Only Graph W starts at the right value and shows the decline from 96 to 48 to 24 every hour, corresponding to the half-life.