SAT Question 9a144a01: Answer, Explanation & Desmos Solution

Which of the following is true about the values of $2^{x}$ and $2 x + 2$ for $x > 0$ ?

Difficulty:Medium

For all $x > 0$ , it is true that $2^{x} < 2 x + 2$ .

For all $x > 0$ , it is true that $2^{x} > 2 x + 2$ .

There is a constant $c$ such that if $0 < x < c$ , then $2^{x} < 2 x + 2$ , but if $x > c$ , then $2^{x} > 2 x + 2$ .

There is a constant $c$ such that if $0 < x < c$ , then $2^{x} > 2 x + 2$ , but if $x > c$ , then $2^{x} < 2 x + 2$ .

Explanation