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