Step 1 :The initial amount of the drug injected can be found by evaluating the function at \(h=0\).
Step 2 :Substitute \(h=0\) into the function \(D(h)=50 e^{-0.2 h}\) to get \(D(0)=50 e^{-0.2*0}=50.0\).
Step 3 :The amount of the drug in the bloodstream after 7 hours can be found by evaluating the function at \(h=7\).
Step 4 :Substitute \(h=7\) into the function \(D(h)=50 e^{-0.2 h}\) to get \(D(7)=50 e^{-0.2*7}\) which is approximately 12.33.
Step 5 :Final Answer: The initial amount of the drug injected is \(\boxed{50.0}\) milligrams and the amount in the bloodstream after 7 hours is approximately \(\boxed{12.33}\) milligrams.