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The number of people employed as medical assistants in a country was 373 thousand in 2003. By the year 2013​, this number is expected to rise to 591 thousand. Let y be the number of medical assistants​ (in thousands) employed in the country in the year​ x, where x=0 represents 2003. a. Write a linear equation that models the number of people​ (in thousands) employed as medical assistants in the year x. b. Use this equation to estimate the number of people who will be employed as medical assistants in the year 2012.

Respuesta :

a) The linear function is: [tex]y = 21.8x + 373[/tex]

b) The estimate for the number of people employed in 2012 is of 569.2.

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A linear function has the following format:

[tex]y = mx + b[/tex]

In which

  • m is the slope, that is, how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0.

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Item a:

  • During the first year of observation, the number of people, in thousands of dollars, was of 373. Thus, the y-intercept is [tex]b = 373[/tex]
  • In 10 years, it changed from 373 to 591, thus, the slope is:

[tex]m = \frac{591 - 373}{10} = 21.8[/tex]

The function is:

[tex]y = 21.8x + 373[/tex]

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Item b:

2012 is 9 years after 2003, thus, this is [tex]y(9)[/tex]

[tex]y(9) = 21.8(9) + 373 = 569.2[/tex]

The estimate for the number of people employed in 2012 is of 569.2.

A similar problem is given at https://brainly.com/question/24742848

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