To analyze the growth rates of Function #1 (linear) and Function #2 (exponential), we can consider their characteristics:
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Linear Function (Function #1): The growth rate remains constant; it increases by the same amount for each unit increase in \(x\).
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Exponential Function (Function #2): The growth rate increases faster than linear growth; it grows by a percentage of its current value, causing it to surpass linear functions as \(x\) increases.
Given that the problem states that initially Function #1 has the greater growth rate, but eventually after a certain point \(x=32\), the growth rate of Function #2 surpasses the growth rate of Function #1, the correct response is:
Initially, Function #1 has the greater growth rate. After \(x=32\), the growth rate of Function #2 surpasses the growth rate of Function #1.