Sales of CRT and LCD Screens In the early 21 st cenJury, LCD...

Sales of CRT and LCD Screens In the early 21 st cenJury, LCD monitors were a new technology that replaced -CRT (cathode ray tube) monitors. In $2002,75$ million CRT -nonitors were sold and only 29 million flat LCD (liquid erystal display) monitors were sold. By $2006,$ the numbers -vere 45 million for CRT monitors and 88 million for LCD nonitors. (Source: International Data Corporation.) -a) Find a linear function $C$ that models these data for CRT monitors and another linear function $L$ that models these data for LCD monitors. Let $x$ be the year. - b) Determine the year when sales of these two types of monitors were equal.

Sales of CRT and LCD Screens In the early 21 st cenJury, LCD monitors were a new technology that replaced
-CRT (cathode ray tube) monitors. In $2002,75$ million CRT
-nonitors were sold and only 29 million flat LCD (liquid erystal display) monitors were sold. By $2006,$ the numbers
-vere 45 million for CRT monitors and 88 million for LCD nonitors. (Source: International Data Corporation.)
-a) Find a linear function $C$ that models these data for CRT monitors and another linear function $L$ that models these data for LCD monitors. Let $x$ be the year.
- b) Determine the year when sales of these two types of monitors were equal.

Key Concepts

Solving Linear Equations

Solving linear equations, typically involving operations like addition, subtraction, multiplication, and division, is a fundamental algebraic skill. It allows one to isolate variables and find exact solutions for equations, a process that is consistently applied when working with linear models and analyzing their intersections.

Linear Functions

A linear function expresses the relationship between two quantities using a constant rate of change, generally written in the form y = mx + b, where m is the slope and b is the y-intercept. This form is essential for modeling relationships where the change between variables is uniform, resulting in a straight line when graphed.

Calculating Slope from Two Data Points

Determining the slope of a linear function involves calculating the rate of change between two points on the line. This is done using the formula (y? - y?)/(x? - x?), which quantifies how much the output variable changes per unit change in the input variable. This concept is key for deriving an accurate linear model from given data.

Determining the Intersection of Linear Functions

Finding the intersection of two linear functions involves equating them and solving for the variable where their outputs are equal. This process is crucial for identifying when two trends or models yield the same value, such as finding the point in time when two differing processes or behaviors converge.

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