Sensory systems continuously adapt their responses based on the frequency of stimuli they encounter. Our goal is to develop a clear understanding of how populations of cortical neurons adapt to varying sensory environments. Recent experiments in the mouse primary visual cortex (V1) have shown a remarkable finding: the magnitude of population responses follows a power law with respect to stimulus frequency. This power law is universal, with the same exponent observed across different statistical environments, enabling predictions of population responses to new environments and allowing the brain to estimate the likelihood of stimuli. While this power law remains consistent across distributions of the same class of stimuli, the exponent varies for different types of stimuli (e.g., gratings versus natural images). Furthermore, the power law breaks down in environments where the frequency of parameterized stimuli changes abruptly. To address these phenomena, we employed a computational approach to answer three key questions: Why does a power law emerge? Why does the exponent change with stimulus type? And why does the law break down in extreme environments? Using an efficient coding framework, we developed a model where neurons adjust their firing rates through multi-objective optimization. This approach aims to enhance both stimulus detection and discrimination while minimizing overall network activity. Our model replicates three key experimental findings across a wide range of parameters without the need for fine-tuning. Overall, we find that the essential features of the data can be explained as a trade-off between representation fidelity and metabolic cost.