22
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Comparing Exponential, Linear, and Quadratic Growth

Question 22 • High School Math 2 A

Compare the functions y = 2x2 and y = 2x. Which of the following statements are true? Check all that apply.

Answer
A
For any x-value, the y-value of the exponential function is always greater.
B
For any x-value, the y-value of the exponential function is always smaller.
C
For some x-values, the y-value of the exponential function is smaller.
D
For some x-values, the y-value of the exponential function is greater.
E
For any x-value greater than 7, the y-value of the exponential function is greater.
F
For equal intervals, the y-values of both functions have a common ratio.

Explanation

Compare the functions 2x² and 2ˣ at different x-values. At x = 3, the values are 18 and 8, so the exponential function is smaller for some x-values (C). At x = 2, the values are 8 and 4, so it is greater for some x-values (D). For x > 7, 2ˣ stays greater than 2x²; for example, at x = 8 the values are 256 and 128 (E). The functions are not ordered the same way for every x, and a quadratic does not have a common ratio over equal intervals, so A, B, and F are false.

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