Answer:
(a) 40 milligrams
(b) 1.21 milligrams
Step-by-step explanation:
Exponential Function
It's commonly used to model real situations in life, like this one proposed in the question where the number of milligrams of a drug D(h) in a patient's bloodstream h hours after the drug is injected is modeled by the following function.
[tex]D(h) =40e^{-0.5h}[/tex]
(a) The initial amount injected to the patient can be found when h=0
[tex]D(0) =40e^{-0.5(0)}=40e^{0}=40[/tex]
Initial amount: 40 milligrams
(b) Let's plug h=7
D(7) =40e^{-0.5(7)}=40e^{-3.5}=1.21
The amount in the bloodstream after 7 hours is 1.21 milligrams
