comparing rates of change\n\nwhich function increases at a faster rate on 0 to infinity, $f(x) = x^2$ or…

comparing rates of change\n\nwhich function increases at a faster rate on 0 to infinity, $f(x) = x^2$ or $g(x) = 2^x$? explain your reasoning.

comparing rates of change\n\nwhich function increases at a faster rate on 0 to infinity, $f(x) = x^2$ or $g(x) = 2^x$? explain your reasoning.

Answer

Answer:

$g(x) = 2^x$ increases at a faster rate on the interval $[0, \infty)$ because exponential functions eventually grow faster than any polynomial function as $x \to \infty$.