Question

Annual Salary A librarian's salary was $\$ 25,000$ in 2004 and $\$ 27,500$ in 2006 . The librarian's salary follows a linear growth pattern. What will the librarian's salary be in 2008$?$

Name: Problem 46, Chapter 1: Precalculus with Limits : A Graphing Approach
Uploaded: 2020-09-06T22:39:30-08:00
Duration: 2 min 28 s
Channel: Amy Jiang
Description: Annual Salary A librarian's salary was 25,000 in 2004 and 27,500 in 2006 . The librarian's salary follows a linear growth pattern. What will the librarian's salary be in 2008?

   Annual Salary A librarian's salary was $\$ 25,000$ in 2004 and $\$ 27,500$ in 2006 . The librarian's salary follows a linear growth pattern. What will the librarian's salary be in 2008$?$

Precalculus with Limits : A Graphing Approach

Ron Larson, Robert… 5th Edition

Chapter 1, Problem 46

Instant Answer

Solved by Expert Amy Jiang

09/06/2020

Step 1

The slope is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where $ (x_1, y_1) $ and $ (x_2, y_2) $ are two points on the line. In this case, the points are (2004, 25000) and (2006, 27500). So, we have: \[ m = \frac{27500 - 25000}{2006 - 2004} Show more…

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Annual Salary A librarian's salary was $\$ 25,000$ in 2004 and $\$ 27,500$ in 2006 . The librarian's salary follows a linear growth pattern. What will the librarian's salary be in 2008$?$

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Key Concepts

Linear Functions

Linear functions are mathematical models that describe a straight-line relationship between two variables, typically expressed in the form y = mx + b. This concept is key for modeling consistent growth or decline, such as predicting salary changes over time, by linking each input value (time) with a corresponding output value (salary).

Slope

The slope in a linear function represents the rate of change between the variables. It indicates how much the dependent variable (salary) increases or decreases for each unit increase in the independent variable (time), a crucial concept for understanding and calculating increments in scenarios involving steady growth.

Extrapolation

Extrapolation is the process of estimating the value of a variable outside the range of known data by assuming that the established trend continues. This concept is essential when using linear models to predict future values, like estimating a salary beyond the provided time frame.

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