Exponential Function

9
advanced-math

Identify the equation for the graph passing through (0,2)(0, 2) and (1,10)(1, 10).

A

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

B

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

C

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

D

y=2+8xy = 2 + 8x

Correct Answer: A

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

  1. Find a: Y-intercept is 2, so a=2a=2.
  2. Find b: yy goes from 2 to 10. 2×b=10b=52 \times b = 10 \implies b=5.
  3. Equation: y=2(5)xy = 2(5)^x.

💡 Strategic Tip:b=y2/y1b = y_2 / y_1 when Δx=1\Delta x = 1.

Choice B is incorrect because it swaps aa and bb. Choice D is incorrect because it is linear.