(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) 20 1 10.2 c(t) = Calculate the parameters co and k, that fit the model to this data. Co =D and k,
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
11-2:
![**Question A: Understanding Constants in Pharmacokinetics**
- **Option A:** The constant \( k_1 \) represents the initial concentration of the drug in the blood, and constant \( c_0 \) represents the rate of elimination.
- **Option B:** The constant \( k_1 \) represents the rate of elimination and constant \( c_0 \) represents the final concentration of the drug in the blood.
- **Option C:** The constant \( k_1 \) represents the rate of elimination and constant \( c_0 \) represents the initial concentration of the drug in the blood.
- **Option D:** The constant \( k_1 \) represents the rate at which the drug is entering the blood, and constant \( c_0 \) represents the initial concentration of the drug in the blood.
**Question B: Data Analysis and Model Fitting**
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 \( c_0 \) and \( k_1 \).
| \( t \) (hrs) | \( c(t) \) (mg/liter) |
|---------------|-----------------------|
| 0 | 20 |
| 1 | 10.2 |
\[ c(t) = \]
**Task: Calculate the parameters \( c_0 \) and \( k_1 \) that fit the model to this data.**
\[ c_0 = \, \text{[Blank]} \]
\[ k_1 = \, \text{[Blank]} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7dce3dae-6456-4f3a-a2bd-6bde155fd2f1%2F9a5c5066-50af-4da3-88a9-fa0511d60adf%2Fys8lx73_processed.png&w=3840&q=75)
![**Modeling Drug Concentration in Blood**
When you are modeling the concentration of a drug in a person's blood after they take one pill, we assume that once ingested, the drug enters their bloodstream instantaneously. The drug is modeled to exhibit first-order elimination kinetics, which is described by the following differential equation:
\[
\frac{dc}{dt} = -k_1 c
\]
where \( c(0) = c_0 \).
**Explanation of the Equation:**
- \( \frac{dc}{dt} \) represents the rate of change of the drug concentration in the blood over time.
- \( k_1 \) is a constant that represents the rate of elimination of the drug.
- \( c \) is the concentration of the drug in the blood.
- \( c_0 \) is the initial concentration of the drug right after the pill is taken.
This model helps in understanding how the drug concentration decreases over time, an important consideration for effective dosing regimens.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7dce3dae-6456-4f3a-a2bd-6bde155fd2f1%2F9a5c5066-50af-4da3-88a9-fa0511d60adf%2Fo15kom_processed.png&w=3840&q=75)
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