3Dr. Priya Mehta, a virologist, is testing a new antiviral compound on cell cultures infected with a synthetic virus. She starts with 1,200 infected cells. The compound reduces the viral load by 60% each hour. After how many full hours will fewer than 100 infected cells remain?

["Title: Combined: How 3Dr. Priya Mehta’s Antiviral Compound Reduces Viral Load Hour by Hour", "In the cutting-edge world of virology, precision and timing are critical when developing new antiviral therapies. Dr. Priya Mehta, a dedicated virologist at a leading research institute, is pioneering innovative treatments using a synthetic virus engineered for controlled studies. Her latest experiment uses a novel antiviral compound designed to combat emerging viral threats.", "The Experiment: Tracking Viral Decline in Cell Cultures", "Dr. Mehta begins with a single culture of 1,200 infected human cells, each harboring a synthetic virus capable of replica within the host cells. To simulate viral spread and measure the efficacy of her new antiviral compound, she introduces a tested antiviral agent directly into the culture. The key mechanism of action: the compound reduces the number of virions—measured as infected cell equivalents—by 60% per hour.", "This exponential decay means the viral load decreases geometrically. Mathematically, the remaining infected cells after t hours follows the formula:", "[\nC(t) = C_0 \ imes (0.4)^t\n]", "Where:\n- (C(t)) = infected cells remaining after t hours\n- (C_0) = initial infected cell count = 1,200\n- 0.4 = retention fraction (since 60% reduction leaves 40% of the virus)", "We want to find the smallest whole number of hours (t) such that:", "[\n1,200 \ imes (0.4)^t < 100\n]", "Solving the Inequality", "Divide both sides by 1,200:", "[\n(0.4)^t < \frac{100}{1,200} = \frac{1}{12} \approx 0.0833\n]", "Take the logarithm of both sides (base 10 or natural log works—here using base 10):", "[\n\log((0.4)^t) < \log(0.0833)\n]", "Apply power rule of logarithms:", "[\nt \cdot \log(0.4) < \log(0.0833)\n]", "Note: (\log(0.4) \approx -0.39794), and (\log(0.0833) \approx -1.07918)", "Now divide:", "[\nt > \frac{-1.07918}{-0.39794} \approx 2.71\n]", "Since $t$ must be a full hour, the smallest integer greater than 2.71 is 3.", "Conclusion: Full Hours Needed for Viral Decline Below 100 Cells", "Dr. Priya Mehta’s antiviral compound proves highly effective: after 3 full hours, fewer than 100 infected cells remain. This rapid viral load reduction underscores the compound’s potential in curbing viral replication—paving the way for advanced preclinical testing.", "With promising results from cell culture models, Dr. Mehta’s work exemplifies how targeted antiviral research accelerates the fight against viral diseases. Stay tuned as her team advances this therapy toward broader therapeutic applications.", "---", "Keywords: 3Dr Priya Mehta, antiviral compound, synthetic virus, viral load reduction, cell culture research, exponential decay, virology, antiviral therapy, scientific experiment, biopharmaceutical development, leading virologist, 2024 viral research."]