Question

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.
a) 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?
○ y=(159 - 200)t
○ y = \frac{159}{200}t
○ y = \frac{41}{7}t + 159
○ y = \frac{41}{7}t + 200
correct. good job!
b) how many thousands of programming jobs will there be in the year 2021? round to 3 decimal places.

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) $223.429$