# A good approach to mathematical modeling is a two-stage approach, using a verbal description to form a ?, and then, after assiging labels to the quantities, forming an ?.

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Modeling
A good approach to mathematical modeling is a two-stage approach, using a verbal description to form a ?, and then, after assiging labels to the quantities, forming an ?.

2021-03-08
Given is, A good approach to mathematical modeling is a two-stage approach, using a verbal description to form a ?, and then, after assiging labels to the quantities, forming an ?
In two stage process , it is required to make verbal model and then in next stage mathematical model or an algebraic equation using quantities .
Finlly answer is A good approach to mathematical modeling is a two-stage approach, using a verbal description to form a (verbal model) , and then, after assiging labels to the quantities, forming an (algebric equation).

### Relevant Questions

A good approach to mathematical modeling is a two-stage approach, using a verbal description to form a __, and then, after assiging labels to the quantities, forming an __.
Create equations to represent a relationship between quantities.
Define appropriate quantities for $$\cdots$$ descriptive modeling.
Two trains leave a station heading in opposite directions. The first train travels at two-thirds the rate of the second train. If the trains are 360 miles apart after three hours, then at what rate (in mph) was each train traveling?
Mathematical modeling is about constructing one or two equations that represent real life situations. What are these math models used for? Provide at least two equations that can be used in the real world. For example: The equation $$s = 30\ h\ +\ 1000$$ can be used to find your salary given the fact you earn a fixed salary of $1000 per month, plus$30 per hours. Here s represents the total salary and h is the number of hours you worked.
An automobile tire manufacturer collected the data in the table relating tire pressure x​ (in pounds per square​ inch) and mileage​ (in thousands of​ miles). A mathematical model for the data is given by
$$\displaystyle​ f{{\left({x}\right)}}=-{0.554}{x}^{2}+{35.5}{x}-{514}.$$
$$\begin{array}{|c|c|} \hline x & Mileage \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}$$
​(A) Complete the table below.
$$\begin{array}{|c|c|} \hline x & Mileage & f(x) \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}$$
​(Round to one decimal place as​ needed.)
$$A. 20602060xf(x)$$
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,45), (30,51), (32,56), (34,50), and (36,46). A parabola opens downward and passes through the points (28,45.7), (30,52.4), (32,54.7), (34,52.6), and (36,46.0). All points are approximate.
$$B. 20602060xf(x)$$
Acoordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2.
Data points are plotted at (43,30), (45,36), (47,41), (49,35), and (51,31). A parabola opens downward and passes through the points (43,30.7), (45,37.4), (47,39.7), (49,37.6), and (51,31). All points are approximate.
$$C. 20602060xf(x)$$
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,45), (45,51), (47,56), (49,50), and (51,46). A parabola opens downward and passes through the points (43,45.7), (45,52.4), (47,54.7), (49,52.6), and (51,46.0). All points are approximate.
$$D.20602060xf(x)$$
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,30), (30,36), (32,41), (34,35), and (36,31). A parabola opens downward and passes through the points (28,30.7), (30,37.4), (32,39.7), (34,37.6), and (36,31). All points are approximate.
​(C) Use the modeling function​ f(x) to estimate the mileage for a tire pressure of 29
$$\displaystyle​\frac{{{l}{b}{s}}}{{{s}{q}}}\in.$$ and for 35
$$\displaystyle​\frac{{{l}{b}{s}}}{{{s}{q}}}\in.$$
The mileage for the tire pressure $$\displaystyle{29}\frac{{{l}{b}{s}}}{{{s}{q}}}\in.$$ is
The mileage for the tire pressure $$\displaystyle{35}\frac{{{l}{b}{s}}}{{{s}{q}}}$$ in. is
(Round to two decimal places as​ needed.)
(D) Write a brief description of the relationship between tire pressure and mileage.
A. As tire pressure​ increases, mileage decreases to a minimum at a certain tire​ pressure, then begins to increase.
B. As tire pressure​ increases, mileage decreases.
C. As tire pressure​ increases, mileage increases to a maximum at a certain tire​ pressure, then begins to decrease.
D. As tire pressure​ increases, mileage increases.
Determine the algebraic modeling a.
One type of Iodine disintegrates continuously at a constant rate of $$\displaystyle{8.6}\%$$ per day.
Suppose the original amount, $$\displaystyle{P}_{{0}}$$, is 10 grams, and let t be measured in days.
Because the Iodine is decaying continuously at a constant rate, we use the model $$\displaystyle{P}={P}_{{0}}{e}^{k}{t}$$ for the decay equation, where k is the rate of continuous decay.
Using the given information, write the decay equation for this type of Iodine.
b.
Use your equation to determine the half-life ofthis type of Fodine, That is, find ‘out how many days it will take for half of the original amount to be left. Show an algebraic solution using logs.
An equation that expresses a relationship between two or more variables, such as $$\displaystyle{H}=\frac{9}{{10}}{\left({220}-{a}\right)}$$,
is called $$\displaystyle\frac{a}{{{a}{n}}} ?.$$ The process of finding such equations to describe real-world phenomena is called mathematical ? .
Such equations, together with the meaning assigned to the variables, are called mathematical ? .
? An equation that expresses a relationship between two or more variables, such as $$H = \frac{9}{10} (20 - a)$$ is called a/an ? The process of finding such equations to describe real-world phenomena is called mathematical ? Such equations, together with the meaning assigned to the variables, are called mathematical ?
A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like a stirred tank. Suppose the blood volume is a four-liter tank that initially has a zero concentration of a particular drug. At time $$\displaystyle{t}={0}$$, an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500 mg/L. The inflow rate is 0.06 L/min. Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant. a. Write an initial value problem that models the mass of the drug in the blood, for $$\displaystyle{t}\ \geq\ {0}$$. Solve the initial value problem, and graph both the mass of the drug and the concentration of the drug. c. What is the steady-state mass of the drug in the blood? d. After how many minutes does the drug mass reach 90% of its steady-state level?
Consider that algebraic modeling For the function $$\displaystyle f{{\left({x}\right)}}={34}{\left({1.024}\right)}^{x}$$
1) The function is an increasing exponential function because it is the form $$\displaystyle{y}={a}{b}^{x}$$ and ?