GRE General TestQuantitative ReasoningHard
A scientist is observing the decay of a radioactive substance. The substance decays by half every 15 years. If she starts with 640 grams of the substance, how much will remain after 45 years?
- A320 grams
- B40 grams
- C80 grams
- D160 grams
Show answer & explanationAnswer & explanation
Correct answer: C. 80 grams
The half-life is 15 years. Total time is 45 years. Number of half-lives = 45 / 15 = 3. After 1st half-life: 640/2 = 320g. After 2nd half-life: 320/2 = 160g. After 3rd half-life: 160/2 = 80g.
Why the other options are wrong
- A. This is the amount remaining after 1 half-life (640/2).
- B. This would be the amount after 4 half-lives (640/16).
- D. This is the amount remaining after 2 half-lives (640/4).
Exponential Decay (Half-Life)
Exponential decay with half-life describes the process where a quantity reduces by half over a constant period of time (its half-life).
- Half-life is the time required for a quantity to reduce to half its initial value.
- The decay is exponential, meaning it halves repeatedly.
- Number of half-lives = Total time / Half-life period.
Memory trick: Count the halves, then keep dividing.