Exponential Growth Vs Polynomial Growth

The mathematically buff Doge on the left represents the "weakest" exponential growth (1.0000000000001ˣ), which despite its tiny base still absolutely demolishes the "strongest" polynomial growth (x^99999999999999999) represented by the wimpy Doge on the right. That's the brutal reality of asymptotic behavior—no matter how massive your polynomial exponent is, any exponential function will eventually surpass it. Countless CS students have learned this the hard way when their "optimized" algorithms suddenly collapse under large inputs. Nature knows this trick too—see: bacteria populations vs your immune system's initial response.