Set 1: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. The graph shows exponential decay starting at $y=100$ when $x=0$. 1. Initial Value: The y-intercept is 100, so $a = 100$. 2. Decay Factor: The curve decreases, indicating $0< b < 1$. The shape matches $b = 0.5$. 3. Verify: At $x=1$, $y = 100(0.5)^1 = 50$, which matches the graph. Strategic Tip: For exponential decay, always check that the base is between 0 and 1. Choice B is incorrect because a base greater than 1 represents growth, not decay. Choice C is incorrect because the initial value is 100, not 50. Choice D is incorrect because 1.5 > 1 represents growth.