Answer:
y = 5·3^x
Explanation:
You want the exponential function that has points (-2, 5/9) and (2, 45) on its graph.
Exponential function
An exponential function can be written as ...
y = a·b^x
Parameters
We can find the values of 'a' and 'b' by solving the system of equations we get by substituting the given point values:
5/9 = a·b^-2
45 = a·b^2
Dividing the second equation by the first, we get ...
45/(5/9) = (a·b^2)/(a·b^-2)
81 = 3^4 = b^4 . . . . . simplify
b = 3 . . . . . . . . . match bases
We can use the second equation to find 'a':
45 = a·3^2
5 = a . . . . . . . divide by 9
Equation
The exponential equation you're looking for is ...
y = 5·3^x