Mathematical Reflecations 2

1. a. To find the y-intercept for an exponential equation using the graph, you must extend the graph to the point where the line in question crosses the y-axis. To find the growth factor of an exponential relationship using a graph, you need to compare different values. The easiest way to do this is to divide a y-value by the y-value preceding it, and the quotient is the growth factor. If you are not sure if it is an exponential relationship, it is always good to try this a few times with different numbers.

The y-intercept is most easily found using a table. To do this, you simply find where the value of x is 0 and look at the corresponding value of y. The growth factor is found with a table the same way it is found with a graph. By dividing a value of y by the one before it you find the growth factor of that particular exponential equation.

The third way to find the y-intercept and growth factor of an exponential equation is to look at the equation itself.

The equation above is the standard form for exponential equations. The a is the initial valuue, also known as the y-intercept. The b is the growth factor.

b. Writing and exponential equation is very simple. Since a is the initial value, or y-intercept, you just have to substitute your y-intercept into the equation given in 1.a. The growth factor is represented by b, and so all that is left to do is substitute your second variable in and you have your equation.

2.a. In the standard form of the exponential equation shown in 1.a., the a represents the intial values, or y-intercept. The b, in turn, represents the growth factor of the relationship.

b. On a graph, the a is represented by where the line crosses the y-axis.

c. On a graph, the b is represented by the slope or "shape" of the line.