1a. You can use a table, graph, and an equation to find the y-intercept and growth factor for an exponential relationship. In a table, the y-intercept is when x=0. The growth factor is by what number the y is multiplied by per x. Using a graph, wherever the line crosses the y-axis, that is the y-intercept. The growth factor is the number that is multipled to get from y when x=1 to when x=2, and etc. Also, taking the equation y=a(b^x), a is the starting point, or the y-intercept, and b is the growth factor.
1b. If given that the y-intercept is 2, and the growth factor is 5, we can come up with the exponential equation y=2(5^x). To form the equation, we use the form y=a(b^x). We plug in the y-intercept for a, and the growth factor for b.
2a. In the equation y=a(b^x), a is the y-intercept, and b is the growth factor.
2b. In the graph of y=a(b^x), a is the y-intercept for when x=o.
2c. In the graph of y=a(b^x), b is the multiplier to get from y when x=1 to when x=2, and so on.
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