You have learned to use the point-ratio form to find an exponential curve that fits two data points. You could also use the general exponential equation y = abx and your knowledge of solving systems of equations to find an appropriate exponential curve. For example, you can use the general form to write two equations for the exponential curve through (4, 40) and (7, 4.7):
40 = ab4
4.7 = ab7
Which constant will be easier to solve for in each equation, a or b? Solve each equation for the constant you have chosen. Use substitution and the properties you have learned in this chapter to solve this system of equations. Substitute the values you find for a and b into the general exponential form to write a general equation for this function.
Find a problem in this chapter that you did using the point-ratio form, and solve it again using this new method. Did you find this method easier or more difficult to use than the point-ratio form? Are there situations in which one method might be preferable to the other?