You can put this solution on YOUR website! The general exponential function is: (where b > 0)
To find the particular exponential function for this problem we need to find the values of "a" and "b". To find these values we will take advantage of the fact that if the two given points are to on the graph of this function, then their coordinates must fit the equation.
Let's start with the point (0, -2). If we substitute these values into the general equation for the x and the y we get:
Since any positive number, like b, to the zero power is 1 this becomes:
-2 = a*1
or just
-2 = a
So already we have the value for a.
Now let's use the other point and the value for a to find the value for b:
Solving for b we start by dividing both sides by -2:
Since this becomes:
Multiply both sides by b^2 we get:
Subtracting 1 from each side we get:
Factoring we get:
(4b+1)(4b-1) = 0
From the Zero Product Property we know that one of these factors must be zero. So:
4b+1 = 0 or 4b-1 = 0
Solving these we get:
b = -1/4 or b = 1/4
Since b must be positive we will reject the negative solution. So b = 1/4.
Now that we have "a" and "b" we can write the exponential function:
This may very well be the desired form for the answer. However, since there are powers of 2 in the a and the b we can simplify this some more: (since the rule is to multiply exponents) (since the rule is to add exponents)
So your equation is
or
You'll have to figure out which form is the one your teacher wants to see. (Probably the first one since it "looks" like .
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