Use the table to answer the question. Term Number 1 2 3 4 5 6 7 8 9 Sequence for f(x)=2⋅2x 4 8 16 32 64 128 256 512 1024 Sequence for g(x)=10x+2 12 22 32 42 52 62 72 82 92 The sequences for f(x)=2⋅2x and g(x)=10x+2 are shown. Which of the following statements is true? Statement #1: While the growth rate of g(x) is initially greater than the growth rate of f(x) , the growth rate of f(x) keeps increasing and eventually surpasses the growth rate of g(x) . Statement #2: The growth rate of g(x) is greater than the growth rate of f(x) between the second term and the fifth term. Statement #3: While the growth rate of f(x) is initially greater than the growth rate of g(x) , the growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x) . (1 point) Statement # is true.

Answer 1

Statement #1 is true.

Initially, the growth rate of g(x) is greater than the growth rate of f(x) because g(x) increases by 10 with each term, while f(x) doubles with each term. However, as the terms progress, the growth rate of f(x) increases exponentially because it is being multiplied by 2 each time. Eventually, the growth rate of f(x) surpasses the growth rate of g(x).