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The number (in millions) of employees working in educational services in a particular country was 14.4 in 2005 and 18.8 in 2014. Letx=5 correspond to the year 2005, and estimate the number of employees in 2011. Assume that the data can be modeled by a straight line and that the trend continues indefinitely. Use two data points to find such a line and then estimate the requested quantity Let y represent the number of employees. The linear equation that best models the number of employees (in Millions) is (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to the nearest hundredth as needed.)

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Answer:

  • For 2011 the number of employees will be 17.33 millions.
  • The linear equation that best models the number of employees (in Millions) is [tex]y(x)  = 0.49 * x + 11.94 [/tex]

Step-by-step explanation:

If we wish to model the data as a straight line, we need to use the straight line formula:

[tex]y(x)  = m * x + b[/tex]

where x is the years that have passed since the year 2000, m is the slope of the line and b the value of y when x=0, and y the numer (in millions) of employees.

For x=5 we know that y(5) = 14.4. So, we have:

[tex]y(5)  = m * 5 + b = 14.4 [/tex]

And for x=14 we know that y(14)= 18.8

[tex]y(14)  = m * 14 + b = 18.8 [/tex]

Subtracting the first equation from the second one:

[tex]y(14) - y(5) = m * 14 + b  - m * 5 - b = 18.8 -  14.4 [/tex]

[tex] m * (14  - 5 ) + b - b = 4.4[/tex]

[tex] m * 9  = 4.4[/tex]

[tex] m  = 4.4 / 9[/tex]

[tex] m  = 0.49 [/tex]

Putting this in the second equation

[tex]y(14)  = 0.49 * 14 + b = 18.8 [/tex]

[tex] 6.86 + b = 18.8 [/tex]

[tex]  b = 18.8 - 6.86 [/tex]

[tex]  b = 11.94 [/tex]

So, our equation will be:

[tex]y(x)  = 0.49 * x + 11.94 [/tex]

For 2011 the number of employees will be

[tex]y(11)  = 0.49 * 11 + 11.94 =17.33[/tex]

For 2011 the number of employees will be 17.33 millions.

The linear equation that best models the number of employees (in Millions) is  

Step-by-step explanation:

If we wish to model the data as a straight line, we need to use the straight line formula:

where x is the years that have passed since the year 2000, m is the slope of the line and b the value of y when x=0, and y the numer (in millions) of employees.

For x=5 we know that y(5) = 14.4. So, we have:

And for x=14 we know that y(14)= 18.8

Subtracting the first equation from the second one:

Putting this in the second equation

So, our equation will be:

For 2011 the number of employees will be

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