You are modeling the concentration of a drug in a person's blood after they take one pill. We assume that after they take the pill the drug enters their blood effectively instantaneously. The drug has first order elimination kinetics. Complete parts (a) and (b). O B. The constant k, represents the rate of elimination and constant co represents the final concentration of drug in the blood. OC. The constant k, represents the rate at which drug is entering the blood and constant c, represents the initial concentration of drug in the blood. O D. The constant k, represents the rate of elimination and constant co represents the initial concentration of drug in the blood. (b) You measure the data given on the right for the concentration of the drug in a patient's blood. Write down the solution to the differential equation from part (a) in terms of co and k t (hrs) c(t) (mg/liter) 30 1 21.6 c(t) = -k,t Calculate the parameters co and k, that fit the model to this data. Co =D and k, =O (Type integers or decimal rounded to three decimal places as needed.)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Topic Video
Question

37-please help with highlighted part B (the empty box values). All other answers are correct. Thank you!

dc
= - k, c with c(0) = Co. Choose the correct answer below.
(a) Explain why the concentration of drug in their blood satisfies a differential equation
O A.
The differential equation for a drug with first order elimination kinetics is
dc
= A(t) – kg. As the drug enters the blood effectively instantaneously. There is no further absorption after time t= 0, so A(t) = 0. Thus,
dt
= - koc.
OB.
dc
The differential equation for a drug with first order elimination kinetics is
= A(t) - k, c. As the drug enters the blood effectively instantaneously. There is no further absorption after time t= 0, so A(t) = 0. Thus,
dt
= -k1.
OC.
dc
The differential equation for a drug with first order elimination kinetics is
= A(t) - ko. As the drug enters the blood effectively instantaneously. There is no further absorption after time t= 0, so A(t) = 0. Thus,
dc
= - ko-
dt
OD.
dc
dc
The differential equation for a drug with first order elimination kinetics is
= A(t) - k, c. As the drug enters the blood effectively instantaneously. There is no further absorption after time t= 0, so A(t) = 0. Thus
dt
= - k,c.
dt
Explain what the constants k, and c, represent. Choose the correct answer below.
Transcribed Image Text:dc = - k, c with c(0) = Co. Choose the correct answer below. (a) Explain why the concentration of drug in their blood satisfies a differential equation O A. The differential equation for a drug with first order elimination kinetics is dc = A(t) – kg. As the drug enters the blood effectively instantaneously. There is no further absorption after time t= 0, so A(t) = 0. Thus, dt = - koc. OB. dc The differential equation for a drug with first order elimination kinetics is = A(t) - k, c. As the drug enters the blood effectively instantaneously. There is no further absorption after time t= 0, so A(t) = 0. Thus, dt = -k1. OC. dc The differential equation for a drug with first order elimination kinetics is = A(t) - ko. As the drug enters the blood effectively instantaneously. There is no further absorption after time t= 0, so A(t) = 0. Thus, dc = - ko- dt OD. dc dc The differential equation for a drug with first order elimination kinetics is = A(t) - k, c. As the drug enters the blood effectively instantaneously. There is no further absorption after time t= 0, so A(t) = 0. Thus dt = - k,c. dt Explain what the constants k, and c, represent. Choose the correct answer below.
You are modeling the concentration of a drug in a person's blood after they take one pill. We assume that after they take the pill the drug enters their blood effectively instantaneously. The drug has first order elimination kinetics.
Complete parts (a) and (b).
O B. The constant k, represents the rate of elimination and constant c, represents the final concentration of drug in the blood.
O C. The constant k, represents the rate at which drug is entering the blood and constant co represents the initial concentration of drug in the blood.
O D. The constant k, represents the rate of elimination and constant co represents the initial concentration of drug in the blood.
(b) You measure the data given on the right for the
concentration of the drug in a patient's blood. Write down
the solution to the differential equation from part (a) in
terms of Co and k1.
t (hrs)
c(t) (mg/liter)
30
1
21.6
c(t) = C, e -k,t|
Calculate the parameters cn and k, that fit the model to this data.
Co = and k, = |
(Type integers or decimal rounded to three decimal places as needed.)
Transcribed Image Text:You are modeling the concentration of a drug in a person's blood after they take one pill. We assume that after they take the pill the drug enters their blood effectively instantaneously. The drug has first order elimination kinetics. Complete parts (a) and (b). O B. The constant k, represents the rate of elimination and constant c, represents the final concentration of drug in the blood. O C. The constant k, represents the rate at which drug is entering the blood and constant co represents the initial concentration of drug in the blood. O D. The constant k, represents the rate of elimination and constant co represents the initial concentration of drug in the blood. (b) You measure the data given on the right for the concentration of the drug in a patient's blood. Write down the solution to the differential equation from part (a) in terms of Co and k1. t (hrs) c(t) (mg/liter) 30 1 21.6 c(t) = C, e -k,t| Calculate the parameters cn and k, that fit the model to this data. Co = and k, = | (Type integers or decimal rounded to three decimal places as needed.)
Expert Solution
Step 1

Given that,

The model has an equation c(t)=c0e-k1t

We have to find values of c0 and k1

Given that,

When t= 0 , c(t)=30.

And t =1 , c(t)= 21.6

 

 

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Propositional Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning