6

Set 1: Exponential Functions (Advanced)

Explanation

Answer: A

The graph shows y=k(0.7)xy = k(0.7)^x. If the y-intercept is at (0,140)(0, 140), what is kk?

A.

140

✓ Correct
B.

0.7

C.

98

D.

200

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Use the y-intercept to find kk. 1. Y-intercept: When x=0x = 0, y=k(0.7)0=ky = k(0.7)^0 = k. 2. Given: Y-intercept is 140. 3. Conclusion: k=140k = 140. Strategic Tip: For y=abxy = ab^x, the y-intercept always equals aa. Choice B is incorrect because this is the base, not the coefficient. Choice C is incorrect because this is 140×0.7140\times 0.7, the value at x=1x=1. Choice D is incorrect because this doesn't match the y-intercept.

Key Steps:

The correct answer is 140

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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