Math Reflections 2

1.a. You can use a table to find the y-intercept of an exponential relationship by finding the dependent variable's value when the independent variable's value is 0. When finding the y-intercept of an exponential relationship in a graph, you look to see where the line crosses the y-axis. To find the y-intercept of an exponential equation, you substitute 0 for the independent variable and solve for y. You could also find this by looking for a in the equation y=a(b^X).

You find the growth factor of an exponential relationship from a table by calculating what the dependent variable is multiplied by every time the independent variable increases by 1. To find the growth factor from a graph, find what the dependent variable is multiplied by every time the independent variable increases by 1. This is just like a table, only you use points on the line. The growth factor in the equation is b in the equation y=a(b^X).

1.b. The y-intercept is a in the equation y=a(b^X). The growth factor is b in this equation. To create an exponential relationship's equation, you simply substitute these numbers in for a and b in the equation.

2.a. In the equation y=a(b^X), a is the initial value of the exponential relationship, and b is the growth factor of the exponential relationship.

2.b. In a graph of y=a(b^X), a is the y-intercept.

2.c. In a graph of y=a(b^X), b is the amount y is increased by every x, or the steepness of the line.