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In 1994, the moose population in a park was measured to be 4180. By 1999, the population was measured again to be 3480. If the population continues to change linearly: Find a formula for the moose population, P, in terms of t, the years since 1990. P(t)=? What does your model predict the moose population to be in 2002?​

User Janni Kajbrink
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1 Answer

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23 votes

"If the population continues to change linearly", meaning the pattern or equation is the equation of a straight line.


(\stackrel{x_1}{1994}~,~\stackrel{y_1}{4180})\qquad (\stackrel{x_2}{1999}~,~\stackrel{y_2}{3480}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3480}-\stackrel{y1}{4180}}}{\underset{run} {\underset{x_2}{1999}-\underset{x_1}{1994}}}\implies \cfrac{-700}{5}\implies -140


\begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4180}=\stackrel{m}{-140}(x-\stackrel{x_1}{1994}) \\\\\\ y-4180 = -140x + 279160 \\\\\\ y = -140x+283340~\hfill \boxed{P(t)=-140t+283340}

what if t = 2002?


P(2002)=-140(2002)+283340\implies P(2002)= 3060

User Mohammed Swillam
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