Step 1 :The initial temperature of the soda can be found by substituting \(x=0\) into the function \(T(x)\). This is because the initial temperature is the temperature of the soda at the moment it was placed in the cooler, which corresponds to \(x=0\).
Step 2 :Substituting \(x=0\) into the function \(T(x)\), we get \(T(0)=-8+30 e^{-0.045 \times 0} = 22\). So, the initial temperature of the soda is \(\boxed{22}\) degrees Celsius.
Step 3 :The temperature of the soda after 15 minutes can be found by substituting \(x=15\) into the function \(T(x)\).
Step 4 :Substituting \(x=15\) into the function \(T(x)\), we get \(T(15)=-8+30 e^{-0.045 \times 15} = 7\). So, the temperature of the soda after 15 minutes is \(\boxed{7}\) degrees Celsius.
Step 5 :Final Answer: The initial temperature of the soda is \(\boxed{22}\) degrees Celsius and its temperature after 15 minutes is \(\boxed{7}\) degrees Celsius.