Choice A is the correct answer. Rewrite with a positive exponent.

1. Rewrite: $y = 4(2)^{-x} = 4 \cdot \frac{1}{2^x} = 4(0.5)^x$.
2. Initial Value: When $x=0$, $y = 4$.
3. Direction: Base $0.5 < 1$ means decay (decreasing).
4. Match: Decreasing curve with y-intercept 4.

💡 Strategic Tip: Negative exponent flips the base: $b^{-x} = (\frac{1}{b})^x$.

Choice B is incorrect because negative exponent creates decay, not growth. Choice C is incorrect because the y-intercept is 4, not 2. Choice D is incorrect because both intercept and direction are wrong.