4

Set 2: Exponential Functions (Advanced)

Explanation

Answer: B

The table compares linear and exponential growth:

xxLinearExponential
01010
12020
23040
34080

At what value of xx does exponential first exceed linear by more than 100?

A.

x=5x = 5

B.

x=4x = 4

✓ Correct
C.

x=6x = 6

D.

x=3x = 3

Detailed Explanation

Choice B is correct. Choice B is the correct answer. Extend the patterns and compare. 1. Linear: y=10x+10y = 10 x + 10 (add 10 each step). 2. Exponential: y=10(2)xy = 10(2)^x (multiply by 2 each step). 3. At x=4x=4: Linear = 5050, Exponential = 160160, Difference = 110>100110> 100 ✓ 4. At x=3x=3: Difference = 8040=40<10080- 40 = 40 < 100 ✗ Strategic Tip: Exponential eventually dominates linear, but verify with calculation. Choice A is incorrect because exponential exceeds by more than 100 before x=5x=5. Choice C is incorrect because it exceeds by then, but not "first". Choice D is incorrect because at x=3x=3, difference is only 40.

Key Steps:

The correct answer is x=4x = 4

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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