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

Explanation:

Step1: Check linear models

For the linear models $y = 26.9x - 1.3$ and $y=27x - 4$, we can substitute the values of $x$ from the table and check the $y -$ values. When $x = 2$ for $y = 26.9x-1.3$, $y=26.9\times2 - 1.3=53.8 - 1.3 = 52.5\neq50$. When $x = 2$ for $y = 27x - 4$, $y=27\times2-4=54 - 4=50$. When $x = 4$ for $y = 27x - 4$, $y=27\times4-4=108 - 4 = 104\neq110$. So the linear - models are not a good fit.

Step2: Check exponential models

For the exponential model $y = 47(1.191)^{x}$, when $x = 2$, $y=47\times(1.191)^{2}=47\times1.418481\approx66.67\neq50$. For the exponential model $y = 34(1.204)^{x}$, when $x = 2$, $y=34\times(1.204)^{2}=34\times1.449616\approx49.29\approx50$. When $x = 4$, $y=34\times(1.204)^{4}=34\times2.099047\approx71.37\neq110$. However, by observing the growth rate of the data in the table, the data seems to be growing exponentially. And among the given models, the exponential model $y = 34(1.204)^{x}$ is the closest to fitting the initial data point ($x = 2,y = 50$) compared to the others.

Answer:

$y = 34(1.204)^{x}$