the table shows the estimated number of lines of code written by computer programmers per hour when x people…

Explanation:

Step1: Check for linear - exponential nature

As the number of people working ($x$) increases, the number of lines of code written hourly ($y$) does not increase by a constant amount. For example, when $x$ goes from 2 to 4, $y$ goes from 50 to 110 (increase of 60), when $x$ goes from 4 to 6, $y$ goes from 110 to 160 (increase of 50). So, it is not a linear relationship. We will check exponential models.

Step2: Test exponential models

Let's take the first data - point $(x = 2,y = 50)$ and test the exponential models. For $y = 47(1.191)^x$, when $x = 2$, $y=47\times(1.191)^2=47\times1.418481\approx66.67$. For $y = 34(1.204)^x$, when $x = 2$, $y = 34\times(1.204)^2=34\times1.449616\approx49.29\approx50$.

Step3: Conclusion

Since the model $y = 34(1.204)^x$ gives a value close to the actual value of $y$ for $x = 2$ and the data shows an exponential - like growth pattern (not linear), the best - fitting model is $y = 34(1.204)^x$.

Answer:

$y = 34(1.204)^x$