SOLUTION: How do you get an exponential equation from this points (0,4), (1,6), (2,9), (3,14), (4,21) and (5,31)?

Algebra ->  Equations -> SOLUTION: How do you get an exponential equation from this points (0,4), (1,6), (2,9), (3,14), (4,21) and (5,31)?      Log On


   

Question 841236: How do you get an exponential equation from this points (0,4), (1,6), (2,9), (3,14), (4,21) and (5,31)?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Plot the points on graph paper, but FIRST, TAKE THE LOGARITHMS OF THE y-coordinate VALUES! Pick either base e or base 10, one or the other; not both. You are looking for a line this way:

(Using Natural Logs as an example)
Imagine you have ordered pairs of the form, (x,y).
y=ae%5E%28kx%29
ln%28y%29=ln%28ae%5E%28kx%29%29
ln%28y%29=ln%28a%29%2Bkx%2Aln%28e%29
ln%28y%29=ln%28a%29%2Bkx
highlight%28highlight%28ln%28y%29=kx%2Bln%28a%29%29%29
This is a linear equation, and your set of points might very well fit this model. The vertical axis is for ln%28y%29, the horizontal axis is for x values, the slope is k, and the vertical axis intercept is ln%28a%29.

When you then want this back in the form of an exponential equation, setup your ln(y) equation with the k and intercept you found, and work backward using algebraic steps toward getting y as a function of x.
---- Better yet, once you have the values, just use them to directly form the exponential equation.