2

Set 8: Exponential Functions

Explanation

Answer: B

Evaluate f(x)=10(2)xf(x) = 10(2)^x for x=4x=4.

A.

80

B.

160

✓ Correct
C.

20

D.

10000

Detailed Explanation

Choice B is correct. Choice B is the correct answer. Substitute and calculate. 1. Substitute: f(4)=10(2)4f(4) = 10(2)^4. 2. Exponentiate: 24=162^4 = 16. 3. Multiply: 10×16=16010\times 16 = 160. Strategic Tip: 242^4 is 2×2×2×2=162\times 2 \times 2 \times 2 = 16. Don't do 10×210\times 2 first. Choice A is incorrect because it calculates 10×810\times 8 (232^3). Choice C is incorrect because it calculates 10×210\times 2. Choice D is incorrect because it calculates (10×2)4(10 \times 2)^4 or 10410^4.

Key Steps:

The correct answer is 160

Why others are wrong:
A: Choice A 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.

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