9
advanced-math

The function f(x)=50(1.2)xf(x) = 50(1.2)^x is graphed. What happens to yy as xx increases?

A

yy increases without bound

B

yy approaches zero

C

yy approaches 50

D

yy remains constant at 1.2

Correct Answer: A

Choice A is the correct answer. Analyze the behavior as xx \to \infty.

  1. Base: b=1.2>1b = 1.2 > 1 means exponential growth.
  2. Behavior: As xx increases, (1.2)x(1.2)^x grows larger and larger.
  3. Conclusion: y=50(1.2)xy = 50(1.2)^x increases without bound.

💡 Strategic Tip: For exponential growth (b>1b > 1), the function grows indefinitely as xx increases.

Choice B is incorrect because this describes decay (b<1b < 1), not growth. Choice C is incorrect because 50 is the initial value, not a limiting value. Choice D is incorrect becauseyy is not constant; it grows exponentially.