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advanced-math

Consider the exponential function y=150(1.04)xy = 150(1.04)^x. What is the initial value of this function?

A

1.04

B

150

C

4

D

156

Correct Answer: B

Choice B is the correct answer. The initial value corresponds to aa in the standard form y=abxy = ab^x.

  1. Identify: The standard form of an exponential function is y=abxy = ab^x, where aa is the initial value (y-intercept) and bb is the growth/decay factor.
  2. Compare: In the given equation y=150(1.04)xy = 150(1.04)^x, the coefficient aa is 150.
  3. Conclude: Therefore, the initial value is 150.

💡 Strategic Tip: The initial value is always the number multiplying the power term. It represents the starting amount when x=0x=0.

Choice A is incorrect because 1.04 is the growth factor bb, not the initial value. Choice C is incorrect because 4 represents the percentage growth rate (4%), not the initial value. Choice D is incorrect because 156 is the value when x=1x=1 (150×1.04150 \times 1.04), not the initial value.