8
advanced-math

For f(x)=25(1.1)xf(x) = 25(1.1)^x, which is larger: f(5)f(5) or f(10)f(10)?

A

f(10)f(10)

B

f(5)f(5)

C

They are equal

D

Cannot determine

Correct Answer: A

Choice A is the correct answer. Exponential growth increases with xx.

  1. Base: 1.1>11.1 > 1 means the function is growing.
  2. Comparison: As xx increases, (1.1)x(1.1)^x increases.
  3. Conclusion: f(10)>f(5)f(10) > f(5) since 10>510 > 5.

💡 Strategic Tip: For growth functions (b>1b > 1), larger xx gives larger yy.

Choice B is incorrect because the function is increasing. Choice C is incorrect because different inputs give different outputs. Choice D is incorrect because we can determine this from the growth property.