Advanced MathVery hardWhere exponential overtakes linear
Advanced Math practice question
The functions f and g are defined by f(x) = 3x + 10 and g(x) = 2ˣ. For which of the following is g(x) greater than f(x) for the first time as x increases through the positive integers?
- A. 5Correct
- B. 4
- C. 6
- D. 3
Answer: A. 5
At x = 4, g = 16 < f = 22. At x = 5, g = 32 > f = 25. So x = 5 is the first.
Why the other answers are wrong
- B. 4
- At x = 4, 16 < 22.
- C. 6
- g is already ahead at x = 5.
- D. 3
- At x = 3, 8 < 19.
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