7
advanced-math

A graph of y=a(b)xy = a(b)^x passes through (1,12)(1, 12) and (3,108)(3, 108). Which could be the equation?

A

y=4(3)xy = 4(3)^x

B

y=12(3)xy = 12(3)^x

C

y=3(4)xy = 3(4)^x

D

y=108(12)xy = 108(12)^x

Correct Answer: A

Choice A is the correct answer. Find aa and bb from the points.

  1. Point 1: 12=a(b)1=ab12 = a(b)^1 = ab.
  2. Point 2: 108=a(b)3=ab3108 = a(b)^3 = ab^3.
  3. Divide: 10812=b2=9\frac{108}{12} = b^2 = 9, so b=3b = 3.
  4. Find aa: a(3)=12a(3) = 12, so a=4a = 4.
  5. Verify: 4(3)1=124(3)^1 = 12 ✓, 4(3)3=1084(3)^3 = 108

💡 Strategic Tip: Divide equations to eliminate aa and solve for bb first.

Choice B is incorrect because at x=1x=1, this gives 12(3)=36eq1212(3)=36 eq 12. Choice C is incorrect because the base and coefficient are swapped. Choice D is incorrect because both values are from points, not the equation.