Comparing Exponential and Quadratic Expressions

7.4.4 Comparing Exponential and Quadratic Expressions

7.4.4 • Comparing Exponential and Quadratic Expressions

Cool Down

Tyler completes the table comparing values of the expressions $5 x^{2}$ and $2^{x}$ .

$x$	$5 x^{2}$	$2^{x}$
$1$	$5$	$2$
$2$	$20$	$4$
$3$	$45$	$8$
$4$	$80$	$16$

Tyler concludes that $5 x^{2}$ will always result in greater values than $2^{x}$ for the same value of $x$ . Do you agree? Explain or show your reasoning.

Compare your answer:

Tyler is not correct. For lesser values of $x$ , $5 x^{2}$ results in greater values than $2^{x}$ , but $2^{x}$ eventually results in greater values because it always doubles when $x$ increases by $1$ . When $x = 9$ , $5 (9)^{2} = 405$ and $2^{9} = 512$ , so $2^{9}$ is greater.