Question

(a) use the given points to create a linear model of the data. express numbers as decimals or integers. the linear model in slope - intercept form is y = 41.5x + 824. part 2 of 3 (b) what does the slope mean in the context of this problem? the slope means that the number of prisoners increased at a rate of 41.5 per year during the given time period. correct answer the slope means that the number of prisoners increased at a rate of 41,500 per year during the given time period. part: 2 / 3 part 3 of 3 (c) use the equation in part (a) to predict the number of prisoners in correctional facilities for year 22. the model predicts that there will be approximately prisoners by year 22.

Explanation:

Step1: Identify the linear - model equation

The linear - model equation is $y = 41.5x+824$, where $y$ represents the number of prisoners and $x$ represents the year.

Step2: Substitute the value of $x$

We want to find the number of prisoners in year 22, so we substitute $x = 22$ into the equation.
$y=41.5\times22 + 824$.

Step3: Calculate the value of $y$

First, calculate $41.5\times22=41.5\times(20 + 2)=41.5\times20+41.5\times2=830 + 83=913$.
Then, $y=913+824 = 1737$.

Answer:

1737