A materials scientist is testing a self-healing polymer that repairs 20% of its damage every hour. If a sample starts with 500 units of damage, after how many hours will the damage be less than 100 units? - Sterling Industries

Why Self-Healing Polymers Are Topping Materials Science Headlines
In the evolving space of advanced materials, innovations that mimic nature’s resilience are quietly reshaping industry expectations. Recent work by a materials scientist testing a self-healing polymer reveals a compelling fact: this material repairs 20% of existing damage every hour. If a sample begins with 500 damaged units, how soon can it heal to less than 100? This question reflects broader interest in durable, low-maintenance solutions—exactly the kind of progress gaining traction across manufacturing, packaging, and consumer goods sectors. As sustainability and longevity become key purchasing drivers, breakthroughs like this underscore how science is helping industries reduce waste and extend product life through intelligent material design.

Understanding How the Self-Healing Process Works
A common misconception is that self-healing occurs instantaneously. In reality, repair progresses incrementally, with each hour recovering 20% of the current damage—meaning losses compound but healing slows as material integrity rebuilds. Starting with 500 units, the next stages unfold as follows:

• After 1 hour: 400 units (80% remaining)
• After 2 hours: ~320 units (64% remaining)
• After 3 hours: ~256 units (51.2% remaining)
• After 4 hours: ~205 units (40.8% remaining)
• After 5 hours: ~164 units (32.8% remaining)
• After 6 hours: ~131 units (26.4% remaining)
• After 7 hours: ~105 units (21.6% remaining)
• After 8 hours: ~84 units (16.8% remaining)

Thus, only after 8 hours does damage fall below the critical threshold of 100 units. This dynamic