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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 📰 Software Latex 7701884 📰 Global Energy Hydrogen Ge Hc Stock Price Shocks The Market Heres Why 8592134 📰 The Shocking Truth 2B Hair Is Dm Nicolas Beyond Compare Dont Miss This 4448689 📰 Are Banks Closing For Juneteenth 6246327 📰 Why Virgos Zodiac Stone Could Be Your Life Changing Secret Proven By Experts 6037969 📰 Playstation 2 Games You Need To Experience Theyll Rewire Your Nostalgia 3350429 📰 The Ultimate Black Frame Thats Stealing More Homes Than Cryptocurrency 5640715 📰 Max Oblivion Level 3662186 📰 Wells Fargo Token 5388922 📰 500 Million Won Is Equal To This Massive Amount In Usdshocking Financial Breakdown 8181106 📰 Garage Plans 4412324 📰 The First Episode Of Attack On Titan Stunned Fansheres Why Every Viewers Googling It 7454877 📰 Hulu Cost Explosion Watch To See If 1015 A Month Is Truly Affordable 9413672 📰 Batman The Killing The Gruesome Twist That Left Fans Talkingcomplete Breakdown 1487789 📰 Star Trek Tng 4484993