9
advanced-math

Identify the equation for the table:

xy
010
15
22.5
A

y=10(2)xy = 10(2)^x

B

y=10(0.5)xy = 10(0.5)^x

C

y=5(2)xy = 5(2)^x

D

y=105xy = 10 - 5x

Correct Answer: B

Choice B is the correct answer. Check initial value and ratio.

  1. Initial Value: At x=0,y=10x=0, y=10. So a=10a=10.
  2. Ratio: 5/10=0.55/10 = 0.5, 2.5/5=0.52.5/5 = 0.5. So b=0.5b=0.5.
  3. Equation: y=10(0.5)xy = 10(0.5)^x.

💡 Strategic Tip: If yy is getting smaller by division, it's decay (b<1b < 1).

Choice A is incorrect because it represents doubling. Choice D is incorrect because it is linear subtraction.