Finding an Exponential Function through 2 points

If you want to find the formula through two points like the points below (after hitting select points)

(x1,y1) (x2,y2)
What you are doing then is to divide the two equations:
y2 = c*bx2
y1 = c*bx1
The c's cancel then and we get y2/y1 = bx2-x1 using the division formula for exponents.
Then we cancel the exponent by taking both sides of the equation to the power 1/(x2-x1). As a result the base of the exponential function is (y2/y1)1/(x2-x1)=b.
Then to get the coefficient (c) of the exponential function we use 1 of the two original equations the value for the base substituted in:
y1 = c*bx1
and divide both sides by bx1 to get:
y1/bx1 = c
Thus the formula for the exponential function is c*bx.

To practice recognizing exponential functions there are two points on the graph below. Select the correct base (b) from the list to the right. If you get it wrong it shows you what the wrong slope looks like. If you get it right it gives you a new problem.

X1:?Y1:?
X2:?Y2:?

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Total Time:
Time Left:
Score:
Worth:

You can also play this in game mode by hitting start game. If you get the function right on the first try you will get 3 points. If it takes 2 tries you get 2 points and so on. You have 2 minutes to get the most points you can.

Copyright David B. Sher 2014