Term Number%091%092%093%094%095%096%097%098%099%0D%0ASequence for%0D%0Af(x)=2⋅2x%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A=%0D%0A2%0D%0A⋅%0D%0A2%0D%0A%0D%0A4%098%0916%0932%0964%09128%09256%09512%091024%0D%0ASequence for%0D%0Ag(x)=10x+2%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A=%0D%0A10%0D%0A%0D%0A+%0D%0A2%0D%0A12%0922%0932%0942%0952%0962%0972%0982%0992%0D%0AThe sequences for f(x)=2⋅2x%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A=%0D%0A2%0D%0A⋅%0D%0A2%0D%0A%0D%0A and g(x)=10x+2%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A=%0D%0A10%0D%0A%0D%0A+%0D%0A2%0D%0A are shown. Which of the following statements is true? %0D%0A%0D%0AStatement #1: While the growth rate of g(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A is initially greater than the growth rate of f(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A, the growth rate of f(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A keeps increasing and eventually surpasses the growth rate of g(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A. %0D%0A%0D%0AStatement #2: The growth rate of g(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A is greater than the growth rate of f(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A between the second term and the fifth term. %0D%0A%0D%0AStatement #3: While the growth rate of f(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A is initially greater than the growth rate of g(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A, the growth rate of g(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A keeps increasing and eventually surpasses the growth rate of f(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A.

Question

Term Number%091%092%093%094%095%096%097%098%099%0D%0ASequence for%0D%0Af(x)=2⋅2x%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A=%0D%0A2%0D%0A⋅%0D%0A2%0D%0A%0D%0A4%098%0916%0932%0964%09128%09256%09512%091024%0D%0ASequence for%0D%0Ag(x)=10x+2%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A=%0D%0A10%0D%0A%0D%0A+%0D%0A2%0D%0A12%0922%0932%0942%0952%0962%0972%0982%0992%0D%0AThe sequences for f(x)=2⋅2x%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A=%0D%0A2%0D%0A⋅%0D%0A2%0D%0A%0D%0A and g(x)=10x+2%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A=%0D%0A10%0D%0A%0D%0A+%0D%0A2%0D%0A are shown. Which of the following statements is true? %0D%0A%0D%0AStatement #1: While the growth rate of g(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A is initially greater than the growth rate of f(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A, the growth rate of f(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A keeps increasing and eventually surpasses the growth rate of g(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A. %0D%0A%0D%0AStatement #2: The growth rate of g(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A is greater than the growth rate of f(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A between the second term and the fifth term. %0D%0A%0D%0AStatement #3: While the growth rate of f(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A is initially greater than the growth rate of g(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A, the growth rate of g(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A keeps increasing and eventually surpasses the growth rate of f(x)%0D%0A%0D%0A(%0D%0A%0D%0A)%0D%0A.

Answer 1

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).

Based on the information given in the sequences, we can see that for both f(x) and g(x), as the value of x increases, the values of the functions also increase. However, the rate of increase for f(x) is constant, while the rate of increase for g(x) is increasing.

Therefore, statement #3 is true. The growth rate of g(x) keeps increasing and eventually surpasses the growth rate of f(x).