ITI The admissions office at a public university estimates...

ITI The admissions office at a public university estimates that 65$\%$ of the students offered admission to the class of 2019 will actually enroll. a. Find the linear function $y=N(x),$ where $N$ is the number of students that actually enroll and $x$ is the number of all students offered admission to the class of 2019 . b. If the university wants the 2019 freshman class size to be 1350 , determine how many students should be admitted.

ITI The admissions office at a public university estimates that 65$\%$ of the students offered admission to the class of 2019 will actually enroll.
a. Find the linear function $y=N(x),$ where $N$ is the number of students that actually enroll and $x$ is
the number of all students offered admission to the class of 2019 .
b. If the university wants the 2019 freshman class size to be 1350 , determine how many students should be admitted.

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Key Concepts

Linear Functions

A linear function models a relationship between two variables with a constant rate of change, expressed in the form y = mx + b. In many real-world situations, such as modeling admissions or enrollments, the function is often based on a direct proportional relationship where the intercept is zero and the rate (m) represents the percentage or fraction relating one quantity to another.

Proportional Reasoning

Proportional reasoning involves understanding the constant ratio between two quantities. When a percentage is converted to a decimal, it can be used as the constant multiplier in a linear model. This approach helps in setting up relationships where one quantity is a fixed fraction of another, simplifying the process of predicting one variable based on the other.

Solving Linear Equations

Solving linear equations involves applying algebraic techniques to isolate the variable of interest. When a linear function is defined, such as one representing enrollments as a fraction of admissions, determining the required input value for a desired output involves rearranging the equation and solving for the variable. This process is essential for making predictions or decisions based on the modeled relationship.

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