# A doctor disconnects the intravenous flow of a drug into a patient’s body. After 2 hours, she measures the…

A doctor disconnects the intravenous flow of a drug into a patient’s body. After 2 hours, she
measures the amount of drug in the patient’s body to be 180 mg. Later, 5 hours after
disconnection, she measures 90 mg.
a. Find a linear formula, L(t), that models the amount of drug, mg, in the patient’s system as
a function of time, t hours after disconnection. Show your work (MathType).
b. Find an exponential formula, E(t), that models the amount of drug, mg, in the patient’s
system as a function of time, t hours after disconnection. Show your work (MathType).
c. Graph each of your equations on the same set of axes using Graph(PC)or Grapher (Mac).
(One picture, two graphs in the same picture)
d. Use your formulas to evaluate L(0) and E(0). What do these values represent? Are the
values the same or different? Explain why they must be the same or why they must be
different values.
e. Evaluate L(10) and E(10). What is the meaning of each result? Based on the values for
each, which of the two formulas best models the elimination of the drug from the patient’s
body?
f. Estimate the half-life of E(t) from the graph. Explain how you made your estimate.
Calculate the half-life of the exponential model. Show your work (MathType). Do the results
agree?
g. Calculate the hourly percent decay of the amount of drug in the body. Show your work
(MathType).
h. Estimate
L
t
Δ
Δ
on the one unit interval, 0 1 ≤ ≤t
. Use the graph of E(t) to find another one
unit interval on which
E
t
Δ
Δ
has the same value as
L
t
Δ
Δ
. Explain how you found your