an exponential function and a linear function are graphed below. over which interval does the growth rate of the exponential function continue to exceed the growth rate of the linear function?
a x=0 to x=3
b x=0 to x=1.79
c x=0.38 to x=1.79
d x=1.79 to x= 3

Notice that the growth rate of the exponential function (green) exceed the growth rate of the linear function (blue) when the graph of the exponential function is above the graph of the linear function. From the picture, we can infer that the graph of the exponential function is above the graph or the linear from function from X=0 TO X=0.38 and from X=1.79 TO X=3 (notice that it we don't restrict the domain, it would be from X=1.79 TO INFINITY), so the growth rate of the exponential function exceed the growth rate of the linear function from X=0 TO X=0.38 and from X=1.79 TO X=3. We can also infer that the graph of the exponential function is bellow the graph of the linear function from X=0.38 TO X=1.79, so the growth rate of the linear function exceed the growth rate of the exponential function from X=0.38 TO X=1.79.

To summarize: the growth rate of the exponential function exceed the growth rate of the linear function from X=0 TO X=0.38, then from X=0.38 TO X=1.79 the growth rate of the linear function exceeds the growth rate of the exponential, and finally, from X=1.79 TO X= 3 the growth rate of the exponential function continue to exceed the growth rate of the linear function.

We can conclude that the correct answer is: D X=1.79 TO X= 3

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