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  1. documentclass[12pt]{article}
  2. usepackage{amsmath,amsthm,verbatim,amssymb,amsfonts,amscd, graphicx, multicol, xcolor}
  3. usepackage{fancyhdr,array,tcolorbox,hyperref,faktor}
  4. tcbuselibrary{breakable}
  5.  
  6. newcolumntype{D}{>{centeringarraybackslash}p{3em}}
  7.  
  8. raggedcolumns
  9.  
  10. begin{document}
  11.  
  12. begin{tcolorbox}[breakable, colbacktitle=white!5!red, title=Motivating Exponential Equations, colback=red!10!white]
  13.  
  14. 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.
  15.  
  16. begin{multicols}{3}
  17.  
  18. [
  19. begin{tabular}{|*{2}{D|}}
  20. hline
  21. $t$ & $P_1$ \
  22. hline
  23. 0 & 8 \
  24. hline
  25. 1 & \
  26. hline
  27. 2 & \
  28. hline
  29. 3 & 64 \
  30. hline
  31. end{tabular}
  32. ]
  33.  
  34. columnbreak
  35.  
  36. [
  37. begin{tabular}{|*{2}{D|}}
  38. hline
  39. $t$ & $P_2$ \
  40. hline
  41. 0 & 8 \
  42. hline
  43. 1 & \
  44. hline
  45. 2 & \
  46. hline
  47. 3 & 512 \
  48. hline
  49. end{tabular}
  50. ]
  51.  
  52. columnbreak
  53.  
  54. [
  55. begin{tabular}{|*{2}{D|}}
  56. hline
  57. $t$ & $P_3$ \
  58. hline
  59. 0 & 2 \
  60. hline
  61. 1 & \
  62. hline
  63. 2 & \
  64. hline
  65. 3 & 128 \
  66. hline
  67. end{tabular}
  68. ]
  69.  
  70. end{multicols}
  71.  
  72. Let $P_1 = f(t)$, $P_2 = g(t)$, and $P_3 = h(t)$. Note that $t$ is in years.
  73.  
  74. begin{enumerate}
  75.  
  76. item Determine function formulas that model $P_1$, $P_2$ and $P_3$.
  77.  
  78. item Fill in each of the tables. Determine from the tables when each herd is the same size textit{at the same time}.
  79.  
  80. item Determine algebraically when each pair of herds is the same size.
  81.  
  82. end{enumerate}
  83.  
  84. end{tcolorbox}
  85.  
  86. end{document}
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