3
advanced-mathThe table compares linear and exponential growth:
| Linear | Exponential | |
|---|---|---|
| 0 | 10 | 10 |
| 1 | 20 | 20 |
| 2 | 30 | 40 |
| 3 | 40 | 80 |
At what value of does exponential first exceed linear by more than 100?
A
B
C
D
Correct Answer: B
Choice B is the correct answer. Extend the patterns and compare.
- Linear: (add 10 each step).
- Exponential: (multiply by 2 each step).
- At : Linear = , Exponential = , Difference = ✓
- At : Difference = ✗
💡 Strategic Tip: Exponential eventually dominates linear, but verify with calculation.
Choice A is incorrect because exponential exceeds by more than 100 before . Choice C is incorrect because it exceeds by then, but not "first". Choice D is incorrect because at , difference is only 40.