Advanced MathHardComparing growth over equal intervals
Advanced Math practice question
The function g is defined by g(x) = 2ˣ. Which statement compares the increase in g from x = 1 to x = 3 with the increase from x = 3 to x = 5?
- A. The second increase is 4 times the first.Correct
- B. The two increases are equal.
- C. The second increase is 2 times the first.
- D. The second increase is 8 times the first.
Answer: A. The second increase is 4 times the first.
g(3) − g(1) = 8 − 2 = 6; g(5) − g(3) = 32 − 8 = 24; 24/6 = 4. (Every 2 units of x multiplies g by 4.)
Why the other answers are wrong
- B. The two increases are equal.
- Equal increases would be linear growth; 2ˣ is exponential.
- C. The second increase is 2 times the first.
- Two units of x multiply by 2² = 4, not 2.
- D. The second increase is 8 times the first.
- 8 would be the factor for three units of x.
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