Using Models Use the model given to answer the questions...

Name: Problem 12, Chapter 0: Algebra and Trigonometry
Uploaded: 2019-06-07T18:43:26-08:00
Duration: 3 min 7 s
Channel: Taylor Shimono

Using Models Use the model given to answer the questions about the object or process being modeled. Arizonans use an average of 40 gal of water per person each day. The number of gallons $W$ of water used by $x$ Arizonans each day is modeled by $W=40 x$ . (a) Make a table that gives the number of gallons of water used for each $1000-$ person change in population, from 0 to $5000 .$ (b) If the pressure is $30 \mathrm{lb} / \mathrm{in}^{2},$ what is the depth? (b) What is the population of an Arizona town whose water usage is $120,000$ gal per day?

Using Models Use the model given to answer the questions about the object or process being modeled.

Arizonans use an average of 40 gal of water per person each
day. The number of gallons $W$ of water used by $x$ Arizonans
each day is modeled by $W=40 x$ .
(a) Make a table that gives the number of gallons of water
used for each $1000-$ person change in population, from
0 to $5000 .$
(b) If the pressure is $30 \mathrm{lb} / \mathrm{in}^{2},$ what is the depth?
(b) What is the population of an Arizona town whose water
usage is $120,000$ gal per day?

Key Concepts

Mathematical Modeling

Mathematical modeling involves translating real-world scenarios into mathematical language. It allows complex processes or objects to be represented with equations or functions so that predictions and analyses can be carried out efficiently.

Linear Functions

A linear function represents a relationship where the change between two variables is constant. Typically expressed in the form y = mx + b, when the relationship is directly proportional the model takes the simpler form y = mx, showing that one variable is a constant multiple of the other.

Proportional Relationships

A proportional relationship is a specific type of linear function in which two quantities always have a constant ratio. This means as one value increases, the other increases at a fixed rate, a concept that is widely applicable in scenarios involving constant per-unit rates.

Data Table Construction

Constructing a data table from a function is a method of organizing computed values for different inputs. It helps in visualizing the relationship between variables by listing corresponding pairs of values in a systematic format.

Solving Linear Equations

Solving linear equations is the process of finding the value of an unknown variable in a linear relationship by isolating it on one side of the equation. This technique is essential when reversing a model to determine a quantity that produced a given output.

Unit Analysis

Unit analysis, also known as dimensional analysis, is a technique used to ensure that all measurements in a calculation are consistent with each other. It is particularly important when working with models that involve physical quantities, such as converting between units of pressure, volume, and depth.

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