Question

the number of hate crime convictions in a particular region was 26 convictions in 2006 and has declined by about 4 convictions each year since then. let n be the number of hate crime convictions in the year that is t years since 2006. complete parts (a) through (e). (a) complete the following table to help find an equation for t and n. show the arithmetic that helps to identify the pattern. \

$$\begin{tabular}{|c|c|} \\hline years since 2006 \\\\ t & number of convictions \\\\ n \\\\ \\hline 0 & $\\square - \\square \\cdot 0$ \\\\ \\hline 1 & $\\square - \\square \\cdot 1$ \\\\ \\hline 2 & $\\square - \\square \\cdot 2$ \\\\ \\hline 3 & $\\square - \\square \\cdot 3$ \\\\ \\hline 4 & $\\square - \\square \\cdot 4$ \\\\ \\hline \\end{tabular}$$

$n = \square - \square t$

Explanation:

Step1: Analyze t=0

At t=0 (2006), the number of convictions is 26. So the first blank is 26, the second is 4 (since it declines by 4 each year). So \( 26 - 4 \cdot 0 \).

Step2: Analyze t=1

For t=1, it's 26 - 4*1. So first blank 26, second 4.

Step3: Analyze t=2

For t=2, it's 26 - 4*2. First blank 26, second 4.

Step4: Analyze t=3

For t=3, it's 26 - 4*3. First blank 26, second 4.

Step5: Analyze t=4

For t=4, it's 26 - 4*4. First blank 26, second 4.

Step6: Find the equation

The general form is \( n = 26 - 4t \).

Answer:

For the table:

• t=0: \( 26 - 4 \cdot 0 \)
• t=1: \( 26 - 4 \cdot 1 \)
• t=2: \( 26 - 4 \cdot 2 \)
• t=3: \( 26 - 4 \cdot 3 \)
• t=4: \( 26 - 4 \cdot 4 \)

The equation: \( n = 26 - 4t \)