To compare the growth rates of the two functions based on the characteristics given (Function #1 is linear and Function #2 is exponential), we can analyze their behaviors.
- A linear function (like Function #1) grows at a constant rate, meaning that its slope remains the same as x increases.
- An exponential function (like Function #2), on the other hand, grows at an increasing rate. This means that as x increases, the growth of the exponential function accelerates.
Initially, exponential functions grow faster than linear functions. Over time, however, depending on the specific functions involved, there can be a point where the linear function may surpass the exponential function in terms of steepness or growth after a certain x-value.
Given your options, since Function #2 (the exponential function) starts with a greater growth rate and continues to grow faster initially, your response would likely be:
Initially, Function #2 has the greater growth rate. After x = 32, the growth rate of Function #1 surpasses the growth rate of Function #2.
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