3

Set 17: Exponential Functions

Explanation

Answer: A

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)

✓ Correct
B.

f(5)f(5)

C.

They are equal

D.

Cannot determine

Detailed Explanation

Choice A is correct. 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.

Key Steps:

The correct answer is f(10)f(10)

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

🎯 Keep Practicing!

Master all sections for your best SAT score