In general, linear functions grow at a constant rate, while exponential functions grow at an increasing rate as their input increases. Given that Function #1 is linear (f(x)) and Function #2 is exponential (g(x)), we can deduce how their growth rates compare.
Initially, at small values of x, the linear function can often grow faster than the exponential function. However, as x increases, the exponential function typically surpasses the linear function in growth rate because it grows exponentially faster over time.
From the information provided in your question, it suggests that:
- Initially, Function #1 has the greater growth rate
- After x = 32, the growth rate of Function #2 (the exponential function) surpasses the growth rate of Function #1.
Thus, the correct response would be:
Initially, Function #1 has the greater growth rate. After x = 32, the growth rate of Function #2 surpasses the growth rate of Function #1.
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