suppose there were 159 thousand computer programming jobs in 2010 and that the number increased to 200…

suppose there were 159 thousand computer programming jobs in 2010 and that the number increased to 200 thousand in 2017. model this growth with a linear equation, and use that model to predict the number of computer programming jobs in the year 2021.\na) let y be the number of computer programming jobs in thousands and t be the number of year after 2010. which linear model correctly represents the number of computer programming jobs?\n○ y=(159 - 200)t\n○ y = \\frac{159}{200}t\n○ y = \\frac{41}{7}t + 159\n○ y = \\frac{41}{7}t + 200\ncorrect. good job!\nb) how many thousands of programming jobs will there be in the year 2021? round to 3 decimal places.

suppose there were 159 thousand computer programming jobs in 2010 and that the number increased to 200 thousand in 2017. model this growth with a linear equation, and use that model to predict the number of computer programming jobs in the year 2021.\na) let y be the number of computer programming jobs in thousands and t be the number of year after 2010. which linear model correctly represents the number of computer programming jobs?\n○ y=(159 - 200)t\n○ y = \\frac{159}{200}t\n○ y = \\frac{41}{7}t + 159\n○ y = \\frac{41}{7}t + 200\ncorrect. good job!\nb) how many thousands of programming jobs will there be in the year 2021? round to 3 decimal places.

Answer

Explanation:

Step1: Identify the slope - intercept form

The linear equation is of the form $y = mt + b$, where $m$ is the slope and $b$ is the y - intercept. In 2010 ($t = 0$), $y=159$, so $b = 159$.

Step2: Calculate the slope

The number of jobs in 2010 ($t_1=0,y_1 = 159$) and in 2017 ($t_2 = 7,y_2=200$). The slope $m=\frac{y_2 - y_1}{t_2 - t_1}=\frac{200 - 159}{7}=\frac{41}{7}$. So the linear model is $y=\frac{41}{7}t + 159$.

Step3: Find the value of $t$ for 2021

For 2021, $t=2021 - 2010=11$.

Step4: Substitute $t$ into the equation

Substitute $t = 11$ into $y=\frac{41}{7}t + 159$. Then $y=\frac{41}{7}\times11+159=\frac{451}{7}+159=\frac{451 + 1113}{7}=\frac{1564}{7}\approx223.429$.

Answer:

a) $y=\frac{41}{7}t + 159$ b) $223.429$