Set 14: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Identify when the amount halves. 1. Half-Life: When $(0.5)^{x/3} = 0.5$. 2. Solve: $(0.5)^{x/3} = (0.5)^1$, so $\frac{x}{3} = 1$, giving $x = 3$. 3. Verify: $g(3) = 60(0.5)^1 = 30$ (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 $(0.5)^2 = 0.25$ (quarter, not half). Choice D is incorrect because this doesn't match the equation structure.