6
advanced-math

The graph of y=200(0.9)xy = 200(0.9)^x intersects the y-axis at what point?

A

(0,200)(0, 200)

B

(200,0)(200, 0)

C

(0,0.9)(0, 0.9)

D

(1,180)(1, 180)

Correct Answer: A

Choice A is the correct answer. The y-intercept occurs when x=0x = 0.

  1. Substitute: y=200(0.9)0=200(1)=200y = 200(0.9)^0 = 200(1) = 200.
  2. Point: The graph crosses the y-axis at (0,200)(0, 200).

💡 Strategic Tip: For y=abxy = ab^x, the y-intercept is always (0,a)(0, a) since b0=1b^0 = 1.

Choice B is incorrect because this reverses the coordinates. Choice C is incorrect because 0.9 is the base, not a coordinate. Choice D is incorrect because this is a point on the graph but not the y-intercept.