Sarah is trying to convince her friend Brianna that the exponential function f(x) = 2x will eventually grow larger than the polynomial function g(x) = x30. When Brianna plugs in 5 for x and sees that f(5) = 25 = 32, while g(5) = 530 = 9.3 x 1020, she is really convinced that f will never be larger than g. Which of these is the smallest value of x that Sarah can use to prove that f will grow larger than g?

Question

Sarah is trying to convince her friend Brianna that the exponential function f(x) = 2x will eventually grow larger than the polynomial function g(x) = x30. When Brianna plugs in 5 for x and sees that f(5) = 25 = 32, while g(5) = 530 = 9.3 x 1020, she is really convinced that f will never be larger than g.  Which of these is the smallest value of x that Sarah can use to prove that f will grow larger than g?