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Exponential Functions
BE CAREFUL! When we discuss linear functions, the "b" represents the y-intercept...here, the "a" is the y-intercept.
FOR LINEAR FUNCTIONS, if you don't see a y-intercept, it is actually 0 because you can ADD 0 without changing the value.
FOR EXPONENTIAL FUNCTIONS, if you don't see a y-intercept, it is actually 1 because can MULTIPLY 1 without changing the value.
FOR LINEAR FUNCTIONS, if you don't see a y-intercept, it is actually 0 because you can ADD 0 without changing the value.
FOR EXPONENTIAL FUNCTIONS, if you don't see a y-intercept, it is actually 1 because can MULTIPLY 1 without changing the value.
Exponential growth functions will ALWAYS exceed linear and quadratic functions.
Their growth will be small at first, but it increases very quickly.
Their growth will be small at first, but it increases very quickly.
If b (the growth factor) is 0 < b < 1, the function is modeling EXPONENTIAL DECAY. This is the graph on the left.
If b (the growth factor) is b > 1, the function is modeling EXPONENTIAL GROWTH. This is the graph to the right.
If b is exactly 0, the line is just the x-axis. If b is exactly 1, the line is just a straight line at y = a.
If b is any negative number, the line oscillates (goes up then down then up then down, and so on).
If b (the growth factor) is b > 1, the function is modeling EXPONENTIAL GROWTH. This is the graph to the right.
If b is exactly 0, the line is just the x-axis. If b is exactly 1, the line is just a straight line at y = a.
If b is any negative number, the line oscillates (goes up then down then up then down, and so on).