Question

LOGARITHMS, CONIC SECTIONS, SEQUENCES

Answer 1

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.

$D(h) =40e^{-0.5h}$

(a) The initial amount injected to the patient can be found when h=0

$D(0) =40e^{-0.5(0)}=40e^{0}=40$

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