SOLUTION: Find the equation for an exponential function that passes through the pair of points given below. (-2,2) and (3,3)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the equation for an exponential function that passes through the pair of points given below. (-2,2) and (3,3)      Log On


   

Question 979401: Find the equation for an exponential function that passes through the pair of points given below.
(-2,2) and (3,3)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Pick your base for how to find logarithms, either 10 or e. Use this for the function: y=ab%5Ex. The variable b is the base for the function definition, which will not be expected to be 10 or e.

log%2810%2Cy%29=log%2810%2Ca%29%2Bx%2Alog%2810%2Cb%29

highlight_green%28log%2810%2Cy%29=x%2Alog%2810%2Cb%29%2Blog%2810%2Ca%29%29.
This is a linear equation with slope log%2810%2Cb%29 and vertical axis intercept log%2810%2Ca%29.

The way you use the given points must now be as (-2, log(10,2)) and (3, log(10,3)).

Now use the two points to form a system of two linear equations, and use your already existing skills for linear equations to find ... a and b.
Base ten was chosen for computational purposes. You should not expect b to be 10.