The number of milligrams \( D(h) \) of a drug in a patient's bloodstream \( h \) hours after the drug is injected is modeled by the following function. \[ D(h)=30 e^{-0.35 h} \] Find the initial amount injected and the amount in the bloodstream after 7 hours. Round your answers to the nearest hundredth as necessary. Initial amount:

We begin with the function \[ D(h)=30 e^{-0.35h} \] which models the number of milligrams of the drug in the bloodstream \( h \) hours after injection. ### Step 1. Find the initial amount injected The initial amount corresponds to \( h=0 \). Substitute \( h=0 \) into the function: \[ D(0)=30e^{-0.35(0)}=30e^0=30 \] Thus, the initial amount injected is \( \boxed{30} \) milligrams. ### Step 2. Find the amount in the bloodstream after 7 hours Substitute \( h=7 \) into the function: \[ D(7)=30e^{-0.35(7)}=30e^{-2.45} \] Using a calculator, we find: \[ e^{-2.45} \approx 0.0863 \] Thus, \[ D(7) \approx 30 \times 0.0863 \approx 2.59 \] After 7 hours, the amount in the bloodstream is approximately \( \boxed{2.59} \) milligrams.