4
advanced-math

A graph passes through the points (0,8)(0, 8) and (1,24)(1, 24). Which exponential function matches this data?

A

y=8(3)xy = 8(3)^x

B

y=24(8)xy = 24(8)^x

C

y=8x+16y = 8x + 16

D

y=3(8)xy = 3(8)^x

Correct Answer: A

Choice A is the correct answer. Use the two points to find aa and bb.

  1. Find aa: At (0,8)(0, 8), y=a(b)0=ay = a(b)^0 = a, so a=8a = 8.
  2. Find bb: At (1,24)(1, 24), y=8(b)1=8by = 8(b)^1 = 8b, so 8b=248b = 24, giving b=3b = 3.
  3. Equation: y=8(3)xy = 8(3)^x.

💡 Strategic Tip: The point (1,y)(1, y) directly gives you a×ba \times b, making it easy to solve for bb.

Choice B is incorrect because it reverses the initial value and the point at x=1x=1. Choice C is incorrect because this is a linear function. Choice D is incorrect because it swaps aa and bb.