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This question appears to relate to some problem for which we have no information. The graph of an exponential function shows a doubling at regular intervals. But we are not told what the role is of b, so we cannot comment further.

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Q: What happens to the graph of an exponential function if b is a function between 0 and 1?
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How does the graph of an exponential function differ from the graph of a linear function and how is the rate of change different?

The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.

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