When we look at how fast different kinds of math grow when we count bigger and bigger numbers, we find that some grow much faster than others. Exponential growth starts out slow but gets really fast super quickly. Quadratic growth, on the other hand, gets bigger steadily, but not as fast. So, if we were to line them up from the fastest to the slowest, it would go like this: exponential growth is the fastest, then there's quadratic growth, and last is linear growth. In the end, exponential growth always wins and grows way faster than quadratic growth when we count really high.
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To compare exponential and quadratic growth as x approaches infinity, we see that exponential functions grow much faster than quadratic functions. Exponential functions start slowly but increase at an ever-accelerating rate, while quadratic functions grow at a steady, slower rate. Thus, the order of growth from fastest to slowest is: exponential functions, followed by polynomial functions (like quadratics), and then linear functions. Ultimately, exponential growth always surpasses quadratic growth at infinity.
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