Question

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.

Answer 1

a) The linear function is: $y = 21.8x + 373$

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:

$y = mx + b$

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 $b = 373$
• In 10 years, it changed from 373 to 591, thus, the slope is:

$m = \frac{591 - 373}{10} = 21.8$

The function is:

$y = 21.8x + 373$

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Item b:

2012 is 9 years after 2003, thus, this is $y(9)$

$y(9) = 21.8(9) + 373 = 569.2$

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

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