6
advanced-math

The amount of a drug in the bloodstream decreases by 20% each hour. If the initial dose is 50mg, which equation models the amount A(t)A(t)?

A

A(t)=50(0.20)tA(t) = 50(0.20)^t

B

A(t)=50(0.80)tA(t) = 50(0.80)^t

C

A(t)=50(1.20)tA(t) = 50(1.20)^t

D

A(t)=20(50)tA(t) = 20(50)^t

Correct Answer: B

Choice B is the correct answer. Decay factor is what remains.

  1. Identify Rate: Decrease of 20% means r=0.20r = 0.20.
  2. Calculate Factor: b=1−0.20=0.80b = 1 - 0.20 = 0.80.
  3. Equation: A(t)=50(0.80)tA(t) = 50(0.80)^t.

💡 Strategic Tip: If 20% is lost, 80% remains. Use 0.80.

Choice A is incorrect because 0.20 means losing 80% per hour. Choice C is incorrect because 1.20 implies growth.

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Set 23: Exponential Functions 23