7

Set 4: Exponential Functions

Explanation

Answer: A

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

Multiple Graphs

A.

Decreasing curve starting at 10

✓ Correct
B.

Increasing curve starting at 10

C.

Decreasing curve starting at 0.5

D.

Straight line with slope -0.5

Detailed Explanation

Choice A is correct. 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 because b<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.

Key Steps:

The correct answer is Decreasing curve starting at 10

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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