Set 2: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Find the weekly growth factor. 1. Formula: $N(t) = N_0(b)^t$ where $N_0 = 2000$, $N(5) = 32000$. 2. Solve: $32000= 2000(b)^5$, so $b^5 = 16$. 3. Recognize: $16= 2^4$, but we need $b^5 = 16 = 2^4$, so $b = 2$. 4. Verify: $2000(2)^5 = 2000(32) = 64000$... Strategic Tip: The factor multiplied over all periods is 16, so weekly factor is $\sqrt[5]{16} = 2$. Choice B is incorrect because this is the total growth factor, not weekly. Choice C is incorrect because this would give $2000(4)^5 = 2,048,000$. Choice D is incorrect because the calculation doesn't match.