The number of students who are enrolled in math classes at a...

The number of students who are enrolled in math classes at a local college can be represented by $E=-17 w+600$ where $E$ represents the math class enrollment at the college $w$ weeks after the start of the fall semester. a. Find the total enrollment in math classes at the college at the beginning of the fall semester. (Hint: Because the semester is just starting, $w=0 .)$ b. During which week will the total enrollment be 430 students? c. What will the total enrollment be in math classes after 8 weeks?

The number of students who are enrolled in math classes at a local college can be represented by $E=-17 w+600$ where $E$ represents the math class enrollment at the college $w$ weeks after the start of the fall semester.
a. Find the total enrollment in math classes at the college at the beginning of the fall semester. (Hint: Because the semester is just starting, $w=0 .)$
b. During which week will the total enrollment be 430 students?
c. What will the total enrollment be in math classes after 8 weeks?

Key Concepts

Linear Function Models

A linear function model represents a relationship between two variables where changes in one variable are proportional to changes in the other. It is typically written in the form f(x) = mx + b, where m represents the constant rate of change (slope) and b is the starting value (y-intercept). Such models are widely used in various fields to predict outcomes based on linear trends.

Y-Intercept

The y-intercept is the value of the function when the independent variable is zero. It represents the initial condition or starting value of the system being modeled. In many contexts, this is a crucial piece of information as it provides a baseline from which changes are measured.

Slope

The slope of a linear function quantifies the rate at which the dependent variable changes with respect to the independent variable. It indicates the magnitude and direction of change, with a positive slope showing an increase and a negative slope indicating a decrease per unit change in the independent variable.

Function Evaluation

Function evaluation involves substituting a specific value into the function to calculate the corresponding output. This is a fundamental process in understanding and using mathematical models, as it allows one to determine the value of the dependent variable at any given point of the independent variable.

Solving Linear Equations

Solving linear equations entails using algebraic methods to isolate the variable of interest and determine the value(s) for which the equation holds true. This process is essential in identifying specific instances, such as when a modeled quantity reaches a particular value, within the framework of a linear relationship.

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