Graph with Horizontal Line

5
advanced-math

A graph of y=6(1.5)xy = 6(1.5)^x is shown. At what point does it cross the line y=9y = 9?

A

(1,9)(1, 9)

B

(2,9)(2, 9)

C

(3,9)(3, 9)

D

(0,9)(0, 9)

Correct Answer: A

Choice A is the correct answer. Solve for when y=9y = 9.

  1. Set Equal: 6(1.5)x=96(1.5)^x = 9.
  2. Divide: (1.5)x=96=1.5(1.5)^x = \frac{9}{6} = 1.5.
  3. Recognize: (1.5)x=1.51(1.5)^x = 1.5^1, so x=1x = 1.
  4. Point: (1,9)(1, 9).

💡 Strategic Tip: When the result equals the base, x=1x = 1.

Choice B is incorrect because at x=2x=2, y=6(1.5)2=13.5eq9y = 6(1.5)^2 = 13.5 eq 9. Choice C is incorrect because this would give an even larger yy value. Choice D is incorrect because at x=0x=0, y=6y = 6, not 9.