Final answer:
In any comparison between exponential and linear growth rates, the exponential growth rate will eventually surpass and continue to exceed the linear growth rate over time. For the intervals provided, the exponential function's growth rate exceeds the linear function's growth rate continuously from x = 1.79 to x = 3 due to the nature of exponential growth.
Step-by-step explanation:
The question is asking to identify the interval during which the growth rate of an exponential function exceeds that of a linear function. Exponential growth is characterized by an increasing rate of growth proportional to the current size. Unlike linear growth, which increases at a constant absolute rate, an exponential function grows increasingly faster over time. Therefore, the longer the interval, the more dramatic the difference between the exponential and linear growth rates will be.
Without the specific equations for the exponential and linear functions, we assume classic behavior where the exponential growth rate always exceeds linear growth after a certain point. Hence, given the intervals:
- x = 0 to x = 3
- x = 0 to x = 1.79
- x = 0.38 to x = 1.79
- x = 1.79 to x = 3
The interval where the exponential function's growth rate is guaranteed to surpass the linear function continuously would be x = 1.79 to x = 3. This is because as x increases, the exponential function's rate of growth increases more dramatically compared to the linear function.