An experimental chemist is synthesizing a new polymer that gains 8% of its current mass in each hour due to controlled absorption. Starting at 50 grams, how many full hours are required for the mass to exceed 80 grams?

["Experimental Polymer Gains 8% Mass Per Hour: How Long Until It Exceeds 80 grams?", "In an innovative study within experimental chemistry, researchers are exploring a novel polymer that exhibits controlled mass gain through selective absorption of environmental moisture. Starting initially at 50 grams, this material increases its mass by 8% each hour—reaching a significant milestone: overcoming the 80-gram threshold. But how many full hours does it take for this polymer to grow beyond 80 grams?", "### The Science Behind the Expansion", "Unlike typical polymers, which maintain stable mass under normal conditions, this experimental material undergoes quasi-continuous weight gain through controlled hydration. The absorption process, calibrated precisely in the lab, allows the polymer to absorb water vapor at a rate that increases its total mass by 8% of its current weight every hour.", "This exponential growth behaves mathematically like a compounding process:", "[\nM(t) = M_0 \ imes (1.08)^t\n]", "where:\n- (M(t)) is the mass after (t) hours,\n- (M_0 = 50) grams is the initial mass,\n- (1.08) is the growth factor (100% + 8% gain),\n- (t) is time in full hours.", "### Calculating the Required Time", "We seek the smallest integer (t) such that:", "[\n50 \ imes (1.08)^t > 80\n]", "Divide both sides by 50:", "[\n(1.08)^t > \frac{80}{50} = 1.6\n]", "Take the logarithm of both sides (base 10 or natural log works—we’ll use natural log):", "[\n\ln((1.08)^t) > \ln(1.6)\n]", "[\nt \cdot \ln(1.08) > \ln(1.6)\n]", "Now calculate the values:", "- (\ln(1.08) \approx 0.07696)\n- (\ln(1.6) \approx 0.47000)", "So:", "[\nt > \frac{0.47000}{0.07696} \approx 6.102\n]", "Since (t) must be a full hour (as we count complete hours), we round up to the next whole number:", "[\nt = 7\n]", "### Verification", "Let’s confirm:", "- At (t = 6):\n (50 \ imes (1.08)^6 \approx 50 \ imes 1.5869 = 79.34) grams (below 80)", "- At (t = 7):\n (50 \ imes (1.08)^7 \approx 50 \ imes 1.7138 = 85.69) grams (above 80)", "Thus, 7 full hours are required for the polymer’s mass to exceed 80 grams.", "### Conclusion", "This experimental polymer, gaining 8% of its current mass hourly through controlled absorption, transitions from 50 grams to over 80 grams in just 7 hours—demonstrating remarkable potential for advances in responsive materials. The timeline illustrates both the power of exponential growth and the precision required in materials science for real-time environmental interactions.", "Keywords: experimental chemistry, polymer synthesis, mass gain polymer, controlled absorption, exponential growth, compounding growth rate, materials science, polymer stability, 8% mass increase, full hours calculation."]