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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 📰 Youll Never Guess What 100 Free To Play Games Found In The Top Charts 9281248 📰 Best Wifi Mesh Cnet 4774360 📰 Excel Hack Get The Multiplication Formula That Solves Complex Calculations In Seconds 3135740 📰 A Company Offers A 10 Annual Interest Rate Compounded Quarterly On A Savings Account If An Initial Investment Of 1000 Is Made What Will Be The Balance After 3 Years 7401256 📰 Actually In A Clock Minute Gear Spins 720 Times In 720 Minutes But In A 24 Hour Display Simulated Via Gear Motion 8428050 📰 This Ruby Slot Mastery Change Your Life Forever 9282262 📰 Bruce Lees Secret The Asymmetrical Neck Reflex That No Fitness Guru Teaches You 5286405 📰 Horrible Beauty Unleashed This Horses Sexy Charm Will Blow Your Mind 427548 📰 Calculate The Next Terms 6848157 📰 Tru Culler Secrets The Shocking Hack Every Gamer Needs To Know 7538571 📰 Whats Actually Listed On Craigslist Bostonand Why Its Eating The City 4175078 📰 Pork Milanese Hacks The Secret To Making This Dish Sparkle Like Never Before 6566163 📰 The Ultimate Guide To Savexr That Changed Everything 3014199 📰 Kent Moore Tools 9911749 📰 Connections April 3 4740099