A certain drug, if injected into the blood of a human being, will decay at an instantaneous rate of 2% per hour. An i.v. at a rate of 4 mg per hour is given to the patient. At t=0 there is none of he drug in the bloodstream. ) Create the modeling differential equation for the amount of the drug in the bloodstream, y, at time t. ) Solve the differential equation. :) What is the steady-state level of the drug? 1) When does the drug level reach 90% of the steady-state level?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
icon
Related questions
Question

Please help for c and d.

 

A certain drug, if injected into the blood of a human being, will decay at an instantaneous rate of
2% per hour. An i.v. at a rate of 4 mg per hour is given to the patient. At t = 0 there is none of
the drug in the bloodstream.
a) Create the modeling differential equation for the amount of the drug in the bloodstream, y,
at time t.
b) Solve the differential equation.
c) What is the steady-state level of the drug?
d) When does the drug level reach 90% of the steady-state level?
Transcribed Image Text:A certain drug, if injected into the blood of a human being, will decay at an instantaneous rate of 2% per hour. An i.v. at a rate of 4 mg per hour is given to the patient. At t = 0 there is none of the drug in the bloodstream. a) Create the modeling differential equation for the amount of the drug in the bloodstream, y, at time t. b) Solve the differential equation. c) What is the steady-state level of the drug? d) When does the drug level reach 90% of the steady-state level?
Expert Solution
steps

Step by step

Solved in 6 steps with 5 images

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning