SOLUTION: 2. True or false: The function "f(x) = 3^x" grows three times faster than the function "g(x) = x". Explain.

Question 173599: 2. True or false: The function "f(x) = 3^x" grows three times faster than the function "g(x) = x". Explain.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
2. True or false: The function "f(x) = 3^x" grows three times faster than the function "g(x) = x". Explain.
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What does "grows three times faster" mean? In a math class, things should be clearly defined.
Ignoring that, it's false. There is no definition of "grows three times faster" that would fit this situation. You could say that y = 4x grows three times faster than y = x since the slope is 3 times more than y = x.
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The author of the problem probably meant to point out that 3^x is vastly different from 3x, but even that was done poorly. 3 times faster is 4 times as fast. If not, then 1 time faster would be the same rate, and why would the word "faster" be used?
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