Set 13: Exponential Functions

Explanation

Answer: B

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

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

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

✓ Correct

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

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

Detailed Explanation

Choice B is correct. Choice B is the correct answer. Decay factor is what remains. 1. Identify Rate: Decrease of 20% means $r = 0.20$ . 2. Calculate Factor: $b = 1 - 0.20 = 0.80$ . 3. Equation: $A(t) = 50(0.80)^t$ . 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.

Key Steps:

•

The correct answer is $A(t) = 50(0.80)^t$

Why others are wrong:

A: Choice A is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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