Dr. Liu, a biomedical researcher, models bacterial growth in a petri dish. The bacteria double every 20 minutes. At 1:00 PM, there are 500 bacteria. A treatment is applied at 1:40 PM that kills 30% of the current population immediately, and then further growth resumes. At what time does the population first exceed 100,000?

Mon, 04 May 2026 08:17:08 +0000

**1. Why Are Bacterial Growth Models Gaining Sudden Interest in 2024?**
Recent discussions across science and health communities highlight a growing fascination with how rapidly bacterial colonies develop—especially under controlled conditions. This spike in attention centers on precise, real-world modeling using a simple yet powerful example: a petri dish with bacteria doubling every 20 minutes. A precise timeline—starting with 500 bacteria at 1:00 PM—creates a compelling narrative about exponential growth, treatment impact, and recovery dynamics. As digital health education spreads, users are turning to accurate models like the one developed by researchers such as Dr. Liu to understand infection behaviors, antibiotic responses, and treatment efficacy in a relatable context. **2. Dr. Liu, a Biomedical Researcher, Simulates Bacterial Growth — At 1:00 PM, 500 Bacteria**
Dr. Liu is a leading biomedical researcher applying mathematical modeling to study bacterial population dynamics in controlled petri dish experiments. At exactly 1:00 PM, a controlled culture begins with precisely 500 viable bacteria. The colony follows a strict doubling pattern every 20 minutes, creating an accelerating exponential curve. By 1:40 PM—exactly 40 minutes after treatment initiation—the population reaches 16,000. A targeted intervention immediately eliminates 30% of the current count, a crucial moment that resets growth but doesn’t halt progression. From that point, recovery builds on the surviving fraction, continuing the relentless rhythm of doubling every 20 minutes. **3. The Critical Turning Point: What Happens After the Treatment at 1:40 PM?**
At 1:40 PM, 30% of the 16,000 bacteria are eliminated:
30% of 16,000 = 4,800
Remaining population: 16,000 – 4,800 = 11,200
From this point, growth resumes with exponential acceleration. Each 20 minutes, the survivors double:
- 1:40 PM (post-treatment): 11,200
- 1:60 PM (1:40 + 20 min): 22,400
- 2:20 PM: 44,800
- 2:40 PM: 89,600 The population crosses 100,000 during this second growth cycle—specifically between 2:20 and 2:40 PM—marking the first time it exceeds that key threshold.