An angel investor evaluates a biotech firm whose projected revenue follows the quadratic model \( R(x) = -2x^2 + 40x + 100 \), where \( x \) is years after launch. In which year does revenue peak?

["When Does a Biotech Firm’s Revenue Peak? A Deep Dive Using the Quadratic Model", "For angel investors assessing the financial potential of emerging biotech firms, understanding projected revenue is critical. Many biotech startups rely on innovative therapies or breakthrough technologies, making their financial modeling especially sensitive to timing and market adoption. One widely used tool to forecast revenue is a quadratic model—particularly when early-stage revenue growth is expected to accelerate before tapering off due to market saturation or regulatory hurdles.", "Consider the quadratic revenue function commonly applied in such scenarios:\n[\nR(x) = -2x^2 + 40x + 100\n]\nwhere ( x ) represents the number of years after the firm’s launch, and ( R(x) ) denotes projected annual revenue in millions of dollars.", "### How Quadratic Models Predict Revenue Peaks", "Quadratic revenue models like this one take the classic “hump” shape: initial growth followed by a peak, then gradual decline. This pattern aligns well with biotech investment cycles—initial R&D investment, slow milestone achievement, rapid growth as trials succeed, and eventually stabilization as patents mature and competition increases.", "To find when revenue peaks, we determine the vertex of the parabola, which gives the maximum revenue point in this concave-down graph.", "### Finding the Revenue Peak Year", "For a quadratic function in the form ( R(x) = ax^2 + bx + c ), the vertex occurs at:\n[\nx = -\frac{b}{2a}\n]\nHere, ( a = -2 ), ( b = 40 ). Plugging in:\n[\nx = -\frac{40}{2 \ imes (-2)} = -\frac{40}{-4} = 10\n]\nSo, revenue peaks at year 10 after launch.", "### What This Means for Investors", "In this model, after the 10th year, revenue begins to decline—reflecting real-world challenges such as increased competition, patent expirations, or reduced growth in treatment adoption. For angel investors, this insight helps in setting realistic milestones and understanding when a biotech firm may shift from high-risk, high-reward growth to a more stable, sustainable business model.", "Moreover, the peak at year 10 suggests strong early-stage traction: the firm likely clears key clinical trials, gains regulatory approval, and goes commercializing its therapy within that timeframe. This timing strengthens the firm’s valuation and exit potential—key factors in investment decisions.", "### Conclusion: Strategic Timing in Biotech Investment", "Understanding where revenue peaks using models like ( R(x) = -2x^2 + 40x + 100 ) empowers angel investors to assess risk, timing, and long-term viability. Peak revenue at year 10 indicates that firms investing at the right moment—when development milestones align with market readiness—can maximize returns. For biotech ventures with high upfront costs and extended timelines, recognizing such milestones is not just financial insight; it’s strategic advantage.", "By analyzing the vertex of revenue projections, investors gain a data-driven lens into the delicate balance of science, market dynamics, and timing—making smarter choices in one of the most challenging yet rewarding sectors.", "---", "Key Takeaway:\nIn the biotech revenue model ( R(x) = -2x^2 + 40x + 100 ), revenue peaks at year 10 after launch—offering a critical benchmark for angel investors to time funding, assess performance, and forecast exit potential."]