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:

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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.
The initial amount injected is 30 milligrams, and after 7 hours, there are approximately 2.59 milligrams in the bloodstream.

The number of milligrams of a drug in a patient’s bloodstream hours after the drug is injected is modeled by the following function.

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:

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The number of milligrams of a drug in a patient’s bloodstream hours after the drug is injected is modeled by the following function. 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: