4

Set 7: Exponential Functions

Explanation

Answer: A

Which graph represents the function y=3(0.8)xy = 3(0.8)^x?

Graph Options

A.

Graph with y-intercept 3, decreasing

✓ Correct
B.

Graph with y-intercept 3, increasing

C.

Graph with y-intercept 0.8, decreasing

D.

Graph with y-intercept 0.8, increasing

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Analyze the initial value and direction. 1. Initial Value: When x=0x=0, y=3(0.8)0=3y = 3(0.8)^0 = 3, so y-intercept is 3. 2. Base: 0.8<10.8< 1 means the function is decaying (decreasing). 3. Match: Graph with y-intercept 3 and decreasing curve. Strategic Tip: If b<1b < 1, the graph decreases (decay). If b>1b > 1, it increases (growth). Choice B is incorrect because the base 0.8 < 1 means decay, not growth. Choice C is incorrect because the y-intercept is 3, not 0.8. Choice D is incorrect because both the y-intercept and direction are wrong.

Key Steps:

The correct answer is Graph with y-intercept 3, decreasing

Why others are wrong:
B: Choice B 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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