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begin{tcolorbox}[breakable, colbacktitle=white!5!red, title=Motivating Exponential Equations, colback=red!10!white]

A budding alpaca farm in Canada splits its herd up into 3 groups on January $1^{text{st}}$, 2008. After 3 years, they record the number of alpacas in each herd. Assume each herd grows exponentially.

begin{multicols}{3}

[
begin{tabular}{|*{2}{D|}}
hline
$t$ & $P_1$ \
hline
0 & 8 \
hline
1 & \
hline
2 & \
hline
3 & 64 \
hline
end{tabular}
]

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[
begin{tabular}{|*{2}{D|}}
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$t$ & $P_2$ \
hline
0 & 8 \
hline
1 & \
hline
2 & \
hline
3 & 512 \
hline
end{tabular}
]

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[
begin{tabular}{|*{2}{D|}}
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$t$ & $P_3$ \
hline
0 & 2 \
hline
1 & \
hline
2 & \
hline
3 & 128 \
hline
end{tabular}
]

end{multicols}

Let $P_1 = f(t)$, $P_2 = g(t)$, and $P_3 = h(t)$. Note that $t$ is in years.

begin{enumerate}

item Determine function formulas that model $P_1$, $P_2$ and $P_3$.

item Fill in each of the tables. Determine from the tables when each herd is the same size textit{at the same time}.

item Determine algebraically when each pair of herds is the same size.

end{enumerate}

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end{document}