3
advanced-math

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

C

x=6x = 6

D

x=3x = 3

Correct Answer: B

Choice B is the correct answer. Extend the patterns and compare.

  1. Linear: y=10x+10y = 10x + 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.