Write an exponential function whose graph passes through the given points: (0, -2), and (-2, -32)

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We are looking for an exponential function.  That kind of equation takes the form

`y = ab^x`

We need to solve for a and b.  We will use the points given to create two equations with two unknowns and then solve for a and b.

`-2 = a * b^0`

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We are looking for an exponential function.  That kind of equation takes the form

`y = ab^x`

We need to solve for a and b.  We will use the points given to create two equations with two unknowns and then solve for a and b.

`-2 = a * b^0`

`-32 = a * b^-2`

Since `b^0 = 1`  the first equation tells us that `a = -2`

Now that into the second equation and solve for b.

`-32 = -2*b^-2` 

`16 = b^-2`

Then we flip the equation because `b^-2 = 1/b^2`

`16 = 1/b^2`

`1/16 = b^2`

`b = 1/4`

Our equation is `y = -2*(1/4)^x`

This is an exponential function that passes through (0, -2) and (-2, -32)

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