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? A) 10 B) 100 C) 1000 D) 10000

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Cher

21 February, 11:11

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Maryjane Burke · Answer 1

C) 1000.

2^1000 = 1^301, whereas 1000^30 is 1^90