Graph of y = 2(3)^x

10
advanced-math

Which graph corresponds to y=2(3)xy = 2(3)^x?

A

A line with slope 3.

B

A curve starting at 2 and increasing rapidly.

C

A curve starting at 2 and decreasing towards 0.

D

A curve starting at 3 and increasing.

Correct Answer: B

Choice B is the correct answer. Analyze the features of the function.

  1. Initial Value: a=2a=2, so y-intercept is 2.
  2. Growth/Decay: b=3>1b=3 > 1, so it is increasing (growth).
  3. Shape: Exponential growth curves up rapidly.

💡 Strategic Tip: Growth curves go up to the right. Decay curves go down to the right.

Choice A is incorrect because it is not linear. Choice C is incorrect because it represents decay. Choice D is incorrect because the y-intercept is 2, not 3.