Question

In one part of the world the sea lion population decreased approximately linearly from about 48 thousand in 1988 to about 25 thousand in 2001 find the average rate of change of the sea lion population per year

Answer 1

$\bf ~~~~~~~~~~~~\begin{array}{ccll} \stackrel{x}{year}&\stackrel{y}{lions}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 1988&48000\\ 2001&25000 \end{array}\\\\ -------------------------------\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ 1988}} &,&{{ 48000}}~) % (c,d) &&(~{{ 2001}} &,&{{ 25000}}~) \end{array}$

$\bf slope= {{ m}}\implies \cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \stackrel{\stackrel{average~rate}{of~change}}{\cfrac{25000-48000}{2001-1988}} \implies -\cfrac{23000}{13}$