You can put this solution on YOUR website! Exponential functions are in the form: where k and a are constants. So our task is to find the values of k and a.
We can do this by using the points we know will fit the equation: (1, 3) and (3, 4.32). Let's start with the first point. Substituting the x and y coordinates from (1, 3) for the x and y in we get:
Simplifying we get:
Dividing both sides by a we get:
Now let's do it with the second point. We will use the x and y from (3, 4.32) and the "value" we just got for k: 3/a. Substituting these 3 values into we get:
Simplifying we get:
Dividing both sides by 3 we get:
Finding the square root of both sides we get: or
Since we usually want a > 0 then we may reject the a = -1.2.
As a fraction 1.2 is 6/5. If a = 6/5 then k = 3/(6/5) = 5/2. So our exponential equation is: or ,as decimals, )
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