Question

the function d(h)=5e^{-0.32h} can be used to find the number of milligrams d of a certain drug that is in a patients bloodstream h hours after the drug has been administered. how many milligrams will be present after 1 hour? after 12 hours? after 1 hour, there will be 3.63 milligrams. (round to two decimal places as needed.) after 12 hours, there will be milligrams. (round to two decimal places as needed.)

Explanation:

Step1: Substitute $h = 12$ into the function

Given $D(h)=5e^{- 0.32h}$, when $h = 12$, we have $D(12)=5e^{-0.32\times12}$.

Step2: Calculate the exponent value

First, calculate $-0.32\times12=-3.84$. So $D(12)=5e^{-3.84}$.

Step3: Evaluate the exponential - function value

We know that $e^{-3.84}=\frac{1}{e^{3.84}}$. Using a calculator, $e^{3.84}\approx46.59$, so $\frac{1}{e^{3.84}}\approx\frac{1}{46.59}\approx0.0215$.

Step4: Calculate the value of $D(12)$

Then $D(12)=5\times0.0215 = 0.11$ (rounded to two decimal places).

Answer:

$0.11$