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📰 Solution: Solve $ 3^k - rac{3^{2k}}{2} < -1 $. Let $ x = 3^k $ (note $ x > 0 $). The inequality becomes $ x - rac{x^2}{2} < -1 $, or $ -rac{x^2}{2} + x + 1 < 0 $. Multiply by $-2$ (reversing inequality): $ x^2 - 2x - 2 > 0 $. Solve $ x^2 - 2x - 2 = 0 $: roots are $ x = 1 \pm \sqrt{3} $. Since $ x > 0 $, critical point is $ x = 1 + \sqrt{3} pprox 2.732 $. The quadratic is positive when $ x > 1 + \sqrt{3} $. Since $ x = 3^k $, find smallest $ k $ such that $ 3^k > 1 + \sqrt{3} $. Test $ k = 1 $: $ 3^1 = 3 > 2.732 $. Check $ R(1) = 3 - rac{9}{2} = -1.5 < -1 $. Thus, $ k = oxed{1} $. 📰 Question: A plant biologist models the growth efficiency of a drought-resistant crop with $ G(t) = rac{t^2 - 4}{t - 2} $. Simplify $ G(t) $ and determine its domain. 📰 Solution: Factor numerator: $ t^2 - 4 = (t - 2)(t + 2) $. Thus, $ G(t) = rac{(t - 2)(t + 2)}{t - 2} $. For $ t 📰 Gpc Stock Price Soared 300Heres Why Investors Are Obsessed 8260055 📰 Iron Man Armored Adventures The Most Epic Battles Of His Life Revealed 547498 📰 Nothing To Lose 1997 5800195 📰 Is This Mountain Dew Sweet Lightning The Ultimate Flavor Bomb Find Out Here 3525940 📰 Prayer Mat Praying 8847754 📰 Dookia The Secret Mattress That Changed My Life Forever 3401222 📰 Childrens 3D Pen 7419286 📰 Jisoo Songs 5401216 📰 You Wont Believe What This Mexican Stud Brings To The Table 5653422 📰 Toycam The Hidden Tool Thats Taking Social Media By Storm Heres How 8333659 📰 The Secret Power Of Ood You Need To Know Before Everyone Else 9012115 📰 00006 5500666 📰 5 Step Inside Bowsers Castle The Most Brutal Game Secrets You Never Saw Coming 431890 📰 Zuzu Napa 901818 📰 Microsoft Wireless Display Adapte Finally Effortless Screen Mirroring Perfected 9603313