The number of milligrams $D(h)$ of a certain drug that is in a patient's bloodstream $h$ hours after the drug is injected is given by the following function. \[ D(h)=20 e^{-0.45 h} \] When the number of milligrams reaches 3, the drug is to be injected again. How much time is needed between injections? Round your answer to the nearest tenth, and do not round any intermediate computations.

Step 1 ：The number of milligrams $D(h)$ of a certain drug that is in a patient's bloodstream $h$ hours after the drug is injected is given by the following function: \[D(h)=20 e^{-0.45 h}\]

Step 2 ：We need to find the time $h$ when the drug concentration $D(h)$ reaches 3 mg. This means we need to solve the equation $D(h) = 3$ for $h$.

Step 3 ：This is a simple algebraic problem involving an exponential function. We can solve it using logarithms.

Step 4 ：Solving the equation gives $h$ approximately equal to 4.3.

Step 5 ：Final Answer: The time needed between injections is approximately \(\boxed{4.3}\) hours.