Set 6: Exponential Functions (Intermediate)

Explanation

Answer: B

A radioactive isotope decays such that its mass is halved every unit of time. If the initial mass is 64g, which function models the mass $M(t)$ ?

$M(t) = 64(2)^t$

$M(t) = 64(0.5)^t$

✓ Correct

$M(t) = 32(0.5)^t$

$M(t) = 64(1.5)^t$

Detailed Explanation

Choice B is correct. Choice B is the correct answer. 'Halved' means the factor is $1 /2$ or 0.5. 1. Identify Factor: Halving means multiplying by 0.5 each step. So $b=0.5$ . 2. Identify Initial: Initial mass is 64, so $a=64$ . 3. Form Equation: $M(t) = 64(0.5)^t$ . Strategic Tip: Half-life problems always have a base of $1 /2$ or 0. $5$ (unless written with $e$ ). Choice A is incorrect because base 2 means doubling. Choice C is incorrect because initial mass is 64, not 32. Choice D is incorrect because base 1.5 means growing by 50%.

Key Steps:

•

The correct answer is $M(t) = 64(0.5)^t$

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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Set 6: Exponential Functions (Intermediate)

Detailed Explanation

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