Decisions are driven by diverse needs and drives, with motivational states influencing their relative contribution to behavior as well as shaping the learning and expression of decision-relevant knowledge. We sought to combine experimental observations and theoretical modelling to elucidate how motivational states influence sensory processing and perceptual decision-making. In a two-whisker discrimination task performed by water-restricted mice, we observed that thirst-induced motivation significantly impacts task performance and modulates cortical sensory representations in the somatosensory and premotor cortices. We found that high or low motivational drive is detrimental to both sensory encoding and task performance. Furthermore, we observed that the fast time course of sensorimotor contingency acquisition can be masked by a slower process of allostatic body weight regulation occurring simultaneously, resulting in slower learning curves. Building on these empirical findings, we developed a theoretical model incorporating motivation, effort-reward trade-offs, and sensorimotor association learning. By simulating mice as agents updating their task policy through a random walk biased by their internal model of the task, we successfully replicated the behavioral dynamics and learning trajectories seen in our experiments. Our model is not only capable of reproducing phenomena from our two-whisker task but is also general enough to be applied to a broad spectrum of goal-directed tasks common in systems neuroscience. By connecting sensory processing with effort and motivation, our model offers a straightforward and interpretable framework for understanding mouse goal-directed behavior. This approach could prove to be a valuable tool for explaining behavioral data and refining animal training methodologies.