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). (d) predict the number of hate crime convictions in 2012. the number of hate crime convictions in 2012 will be 2. (type an integer or a decimal.) (e) what is the t-intercept? what does it mean in this situation? select the correct choice and fill in the answer box to complete your choice. (type an ordered pair. type an integer or a decimal.) a. the t-intercept of the model is. the t-intercept estimates the number of years after 2006 when the number of hate crime convictions is zero. b. the t-intercept of the model is. the t-intercept estimates the number of hate crime convictions in 2006.

Explanation:

Part (d)

Step1: Determine t for 2012

2012 is \(2012 - 2006 = 6\) years since 2006, so \(t = 6\).

Step2: Find the linear model

The number of convictions \(n\) as a function of \(t\) is \(n = 26 - 4t\) (since it starts at 26 and decreases by 4 each year).

Step3: Substitute t = 6 into the model

\(n = 26 - 4\times6 = 26 - 24 = 2\).

The t - intercept occurs when \(n = 0\). We set up the equation \(0 = 26 - 4t\).

Step1: Solve for t

\(4t=26\), so \(t=\frac{26}{4} = 6.5\). The t - intercept is the point where \(n = 0\), so the ordered pair is \((6.5,0)\). Option A is correct because the t - intercept (when \(n = 0\)) gives the number of years after 2006 when the number of hate crime convictions is zero. Option B is incorrect because the number of convictions in 2006 is when \(t = 0\) (the y - intercept in terms of n - t, but here we are looking at t - intercept which is when \(n = 0\)).

Answer:

2

Part (e)