10
advanced-math

Which statement about y=7(0.9)x2y = 7(0.9)^x - 2 is true?

A

Horizontal asymptote at y=2y = -2

B

Horizontal asymptote at y=7y = 7

C

The function is increasing

D

The y-intercept is at (0,2)(0, -2)

Correct Answer: A

Choice A is the correct answer. Analyze the function form.

  1. Form: y=abx+ky = ab^x + k where k=2k = -2.
  2. Asymptote: As xx \to \infty, (0.9)x0(0.9)^x \to 0, so y02=2y \to 0 - 2 = -2.
  3. Conclusion: Horizontal asymptote is y=2y = -2.

💡 Strategic Tip: The vertical shift kk determines the asymptote.

Choice B is incorrect because 7 is the coefficient, not the asymptote. Choice C is incorrect becauseb<1b < 1 means decreasing (decay). Choice D is incorrect because y-intercept is 7(1)2=57(1) - 2 = 5, at (0,5)(0, 5).