Set 10: Exponential Functions (Intermediate)

Choice A is correct. Choice A is the correct answer. Work backwards from the remaining percentage. 1. Remaining: 25% = $\frac{1}{4}$ of original. 2. Half-lives: $\frac{1}{4} = (\frac{1}{2})^2$, so 2 half-lives have passed. 3. Time: $2\times 5730 = 11,460$ years. 4. Formula: $0.25= (0.5)^{t/5730}$, solving gives $t = 11,460$. Strategic Tip: 25% = $\frac{1}{4}$ = 2 half-lives have occurred. Choice B is incorrect because this is only 1 half-life (50% remaining). Choice C is incorrect because this is 3 half-lives (12.5% remaining). Choice D is incorrect because this is half of one half-life.