In class we used a graphing calculator to inspect the shapes of growth and decay curves with different bases and initial terms.
In the exponential parent function y = a times b^n . . .
If b is a fraction between zero and 1, the graph shows exponential decay.
If b is greater than 1, the graph shows exponential growth.
If the initial term a is a fraction between zero and 1, the parent graph is compressed vertically, and the slopes at given x's are reduced.
If the initial term a is greater than 1, the parent graph is stretched vertically, and the slopes at given y's are increased.
If the initial term is negative, the parent graph is flipped so that its range falls below the x-axis.
If a constant is added to or subtracted from the parent function, the entire graph is shifted up or down. This is analogous to the value of the y-intercept b in a linear equation altering the height of the line.
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