To compare the growth rates of the two functions based on the graphs described, we need to understand the nature of the functions involved: Function #1 is linear and Function #2 is exponential.
In general:
- A linear function grows at a constant rate. This means that the increase in value is uniform over any interval of x.
- An exponential function grows at a rate that increases rapidly as x increases. This means that after a certain point, the exponential function will begin to grow faster than any linear function.
Based on this explanation, we can deduce that:
- Initially, when x is small, the linear function (Function #1) might grow faster than the exponential function (Function #2).
- However, as x increases, specifically after a certain point (as indicated by x = 32 in the statements), the exponential function will surpass the linear function in terms of growth rate.
Therefore, the correct choice that reflects this comparison 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."
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