ACT (Enhanced)MathematicsMedium
A scientist is observing the decay of a radioactive substance. The mass of the substance, in grams, remaining after 't' days is given by the function M(t) = 200 * (0.5)^(t/10). What is the half-life of the substance?
- A0.5 days
- B200 days
- C10 days
- D20 days
Show answer & explanationAnswer & explanation
Correct answer: C. 10 days
In the exponential decay formula M(t) = M0 * (1/2)^(t/h), M0 is the initial mass, (1/2) is the decay factor (for half-life), and 'h' is the half-life. Comparing this to M(t) = 200 * (0.5)^(t/10), we can see that the half-life 'h' is 10 days.
Why the other options are wrong
- A. This is the decay factor, not the half-life.
- B. This is the initial mass, not the half-life.
- D. Incorrect interpretation of the exponent, possibly multiplying by 2.
Half-Life
The time required for a quantity to reduce to half of its initial value, often used in radioactive decay or drug elimination.
- Characteristic of exponential decay processes.
- The decay factor is typically 1/2 or 0.5.
- Represented as 'h' in M(t) = M0 * (1/2)^(t/h).
Memory trick: Decay is like a fading echo, halving over time.