Multiple Graphs

6
advanced-math

Which graph shows y=10(0.5)xy = 10(0.5)^x?

A

Decreasing curve starting at 10

B

Increasing curve starting at 10

C

Decreasing curve starting at 0.5

D

Straight line with slope -0.5

Correct Answer: A

Choice A is the correct answer. Identify key features.

  1. Initial Value: At x=0x=0, y=10(0.5)0=10y = 10(0.5)^0 = 10.
  2. Base: 0.5<10.5 < 1 means decay (decreasing).
  3. Shape: Exponential decay curve starting at (0,10)(0, 10).

💡 Strategic Tip: Check y-intercept and direction (increasing/decreasing) to match graphs.

Choice B is incorrect becauseb<1b < 1 means decrease, not increase. Choice C is incorrect because the y-intercept is 10, not 0.5. Choice D is incorrect because exponential functions curve, they're not straight lines.