a. Explanation Given information: The concentration of drug in a patient’s blood for t hours is: C = 1 b − a ( e − a t − e − b t ) b > a > 0 Where a , b are parameters depending on patient’s metabolism and kind of drug used. Calculation: The partial differentials for determining the required rates are calculated as: ∂ ∂ a C = ∂ ∂ a { 1 b − a ( e − a t − e − b t ) } = ∂ ∂ a { ( e − a t − e − b t ) b − a } = ∂ ∂ a ( e − a t − e − b t ) ( b − a ) + ( e − a t − e − b t ) ∂ ∂ a ( b − a ) ( b − a ) 2 = ( e − a t ⋅ ∂ ∂ a ( − a t ) − 0 ) ( b − a ) + ( e − a t − e − b t ) ( 0 − 1 ) ( b − a ) 2 = e − a t ( − t ) ( b − a ) + ( e − a t − e − b t ) ( b − a ) 2 = ( e − a t − e − b t ) ( b − b. To determine The rate ∂ C ∂ t while assuming a = ln b t .

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

See similar textbooks

Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

Videos

Question

Chapter 11.5, Problem 39PS

To determine

The rates: ∂C∂a,∂C∂b and ∂C∂t

To determine

The rate ∂C∂t while assuming a=lnbt .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.5, Problem 38PS

Chapter 11.5, Problem 40PS

Students have asked these similar questions

In a study conducted at Dartmouth College, mice with a particular type of cancerous tumor were treated with a chemotherapy drug called Cisplatin. If the volume of one of these tumors at the time of treatment is Vo, then the volume of the tumor t days after treatment is modeled by the function V(t) = = Vo(0.99e- + 0.01e0.239t). -0.1216t 1. Set Vo = 3 and plot V(t) over the interval 0 ≤ t ≤ 16. Appropriately adjust the viewing window to see the behavior of V(t) and sketch the graph below. 2. From the graph, estimate the time at which the volume of the tumor decreased to half its original amount. There are two such times, record each to the nearest whole number. 3. With Vo = 3, write down the equation whose solution gives the time at which the tumor is half its original volume. (Re)write the equation with zero in the right-hand side. 4. Using one of your answers from 2. as to and your equation from 3., apply two steps of Newton's method to better approximate this time. (Round to 3 decimal…

The tensile strength of a synthetic fiber is affected by drying time (x1), drying temperature (x2), and the percentage of cotton in the fiber (x3). The following table shows the data. y 213 220 216 234 230 235 238 230 236 231 243 X₁ 2.0 2.3 2.3 2.5 3.0 3.4 3.4 3.4 4.0 4.0 4.1 Find: a) mathematical model b) estimate the variance X₂ 145 140 140 146 138 135 135 135 141 141 145 X3 13 15 15 18 20 19 19 19 16 16 17 c) confidence interval for beta 2 and alpha 0.05 d) test the significance of the regression.

Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature: that is, F = − kVT, which means that heat energy flows from hot regions to cold regions. The constant k is called the conductivity, which has metric units of J/m-s-K or W/m-K. A temperature function T for a region D is given below. Find the SSF FondSk -KSS VT n dS across the boundary S of D. It may be easier to use the Divergence Theorem and evaluate a triple integral. Assume that k = 1. S S T(x,y,z) = 65e¯x² - y² − z²; net outward heat flux D is the sphere of radius a centered at the origin.

Chapter 11 Solutions

Calculus

Ch. 11.1 - Prob. 1PS Ch. 11.1 - Prob. 2PS Ch. 11.1 - Prob. 3PS Ch. 11.1 - Prob. 4PS Ch. 11.1 - Prob. 5PS Ch. 11.1 - Prob. 6PS Ch. 11.1 - Prob. 7PS Ch. 11.1 - Prob. 8PS Ch. 11.1 - Prob. 9PS Ch. 11.1 - Prob. 10PS

Knowledge Booster

$Calculus$

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.

The rates: ∂ C ∂ a , ∂ C ∂ b and ∂ C ∂ t

Solution Summary: The author explains the partial differentials for determining the required rates.