To find the equation of the exponential function, we can use the general form:
y = ab^x, where "a" is the initial value and "b" is the base.
Given the points (0, -2) and (2, -50), we can substitute these values into the equation to form a system of equations:
For point (0, -2):
-2 = ab^0
-2 = a
For point (2, -50):
-50 = ab^2
Now that we have the value of "a", we can substitute it into the second equation:
-50 = (-2)b^2
Divide both sides of the equation by -2:
25 = b^2
Taking the square root of both sides, we have two possible values for "b":
b = ±5
We can now find the value of "y" when x = -2.
Using the first possible value of "b", b = 5:
y = ab^x
y = (-2)(5)^-2
y = (-2)(1/25)
y = -2/25
Using the second possible value of "b", b = -5:
y = ab^x
y = (-2)(-5)^-2
y = (-2)(1/25)
y = -2/25
Therefore, when x = -2, y can be either -2/25 or -2/25.