5
advanced-math

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)?

A

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

B

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

C

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

D

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

Correct Answer: B

Choice B is the correct answer. 'Halved' means the factor is 1/21/2 or 0.5.

  1. Identify Factor: Halving means multiplying by 0.5 each step. So b=0.5b=0.5.
  2. Identify Initial: Initial mass is 64, so a=64a=64.
  3. Form Equation: M(t)=64(0.5)tM(t) = 64(0.5)^t.

💡 Strategic Tip: Half-life problems always have a base of 1/21/2 or 0.50.5 (unless written with ee).

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%.