8
advanced-math

The function g(x)=60(0.5)x/3g(x) = 60(0.5)^{x/3} represents radioactive decay. What is the half-life?

A

3 units

B

0.5 units

C

6 units

D

1.5 units

Correct Answer: A

Choice A is the correct answer. Identify when the amount halves.

  1. Half-Life: When (0.5)x/3=0.5(0.5)^{x/3} = 0.5.
  2. Solve: (0.5)x/3=(0.5)1(0.5)^{x/3} = (0.5)^1, so x3=1\frac{x}{3} = 1, giving x=3x = 3.
  3. Verify: g(3)=60(0.5)1=30g(3) = 60(0.5)^1 = 30 (half of 60) ✓

💡 Strategic Tip: Half-life is when the exponent of the decay factor equals 1.

Choice B is incorrect because this is the base, not the half-life period. Choice C is incorrect because this would give (0.5)2=0.25(0.5)^2 = 0.25 (quarter, not half). Choice D is incorrect because this doesn't match the equation structure.