3
advanced-math

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

B

0.7

C

98

D

200

Correct Answer: A

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.