Graphing Exponential Growth/Decay

Graphing Exponential Growth/Decay

An exponential function is an equation of the form y = ab^x(with b  > 0). 

          In many cases "a" represents a starting or initial value, "b" represents the multiplier or 

growth/decay factor, and "x" represents the time. 

  

                Example: 

• Graph y = 2^{(x + 3)}
This is not the same as "2^x + 3". In "2^x + 3", the standard exponential is shifted up three units. In this case, the shift in "inside" the exponential. Instead of the "+ 3" shifting the "2^x" up by three, the "+ 3" shifts the "2^x" over sideways by three. The only question is: shifts sideways which way, left or right? The way I keep it straight is to consider one of the basic points on any exponential. When the power is zero, the exponential is 1.  For "2^{(x + 3)}", when is the power zero? When x + 3 = 0, so x = –3. That is, the basic plot point (0, 1) has been shifted to the point (–3, 1), so the graph has been shifted three points to the left: