5
advanced-math

A medication's concentration in blood decreases by 25% every 6 hours. Starting with 800 mg, how much after 24 hours?

A

253.13 mg

B

200 mg

C

400 mg

D

150 mg

Correct Answer: A

Choice A is the correct answer. Apply the decay pattern.

  1. Retention: Decreases 25%, keeps 75% = 0.75 every 6 hours.
  2. Periods: 246=4\frac{24}{6} = 4 periods.
  3. Formula: C(t)=800(0.75)t/6C(t) = 800(0.75)^{t/6} where t=24t = 24.
  4. Calculate: C(24)=800(0.75)4=800(0.31640625)253.13C(24) = 800(0.75)^4 = 800(0.31640625) \approx 253.13.

💡 Strategic Tip: 4 periods of 75% retention = (0.75)40.316(0.75)^4 \approx 0.316.

Choice B is incorrect because this assumes 75% loss, not retention. Choice C is incorrect because this is after 1 period. Choice D is incorrect because the calculation is wrong.