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Time-inconsistency is a characteristic of human behavior in which people plan for long-term benefits but take actions that differ from the plan due to conflicts with short-term benefits. Such time-inconsistent behavior is believed to be caused by present bias, a tendency to overestimate immediate rewards and underestimate future rewards. It is essential in behavioral economics to investigate the relationship between present bias and time-inconsistency. In this paper, we propose a model for analyzing agent behavior with present bias in tasks to make progress toward a goal over a specific period. Unlike previous models, the state sequence of the agent can be described analytically in our model. Based on this property, we analyze three crucial problems related to agents under present bias: task abandonment, optimal goal setting, and optimal reward scheduling. Extensive analysis reveals how present bias affects the condition under which task abandonment occurs and optimal intervention strategies. Our findings are meaningful for preventing task abandonment and intervening through incentives in the real world.