Exponentials
Modeling A Graph
In order to write the function that models an exponential graph, find at least two points on the graph. If the y-intercept (0, a) is easily determined, select it as one of the two points. Otherwise, select two points with integer coordinates to make the computation easier. Then calculate the a and b-values.
Example Write a function to model the graph.
Step 1. Determine the y-intercept.
Notice (0, 4) is on the graph, therefore a = 4 and y = 4 . bx
Step 2. Determine another point on the graph and substitute it into x and y in the equation, then solve for b.
Notice (1, 8) is on the graph, use it in the equation.
8 = 4 . b1
2 = b
Therefore, y = 4 . 2x models this graph.