7

Set 10: Exponential Functions (Intermediate)

Explanation

Answer: B

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

Graph of y = 2(3)^x

A.

A line with slope 3.

B.

A curve starting at 2 and increasing rapidly.

✓ Correct
C.

A curve starting at 2 and decreasing towards 0.

D.

A curve starting at 3 and increasing.

Detailed Explanation

Choice B is correct. 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.

Key Steps:

The correct answer is A curve starting at 2 and increasing rapidly.

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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