Question

Slope-rate of change- “if there were 12,000 in the Atlantic Ocean in 1950 and there are 3,600 dolphins today, what is the yearly rate of change?” I don’t even know where to start. I need help.

Answer 1

`\bf \begin{array}cc \cline{1-2} \stackrel{x}{year}&\stackrel{y}{dolphins}\\ \cline{1-2} &\\ 1950&12000\\ 2018&3600 \\&\\ \cline{1-2} \end{array}~\hspace{5em}(\stackrel{x_1}{1950}~,~\stackrel{y_1}{12000})\qquad (\stackrel{x_2}{2018}~,~\stackrel{y_2}{3600}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3600-12000}{2018-1950}\implies \cfrac{-8400}{68}~~\approx~~ \stackrel{\textit{rate of change}}{-123.53}`

-8400/68 simplifies to to -2100/17, dolphins/year, so 2100 less dolphins every 17 years.

and we can just divide those to get the decimal amount of -123.53, which means, 123.53 less dolphins every year.

of course, there's no such a thing as 0.53 of a dolphin, so, we can say "about" 123 less dolphins per year.