Question

The crime rate in New York City has been steadily dropping over the past decades. In 1970, the murder rate was 15.8 per 100,000 people. In 2012, it had dropped to 3.5 per 100,000 people. What was the rate of decline?

Answer 1

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------$

$\bf \begin{array}{ccll} \stackrel{period}{year}&\stackrel{per~10000}{crime}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1970&15.8\\ 2012&3.5 \end{array} \implies \cfrac{f(b)-f(a)}{b-a}\implies \cfrac{3.5-15.8}{2012-1970}\implies -\cfrac{12.3}{42} \\\\\\ -0.2929\frac{\stackrel{per~10000}{crime}}{year}$