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Tree Growth Simulation

Tree Growth Simulation
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2015-11-03 04:49
FunctionSlider AnimationGraphing
In collections CCSS Support Math II Unit 2
This example demonstrates the growth process of a tree over time. It involves the concept of exponential functions, and by adjusting the time slider, one can observe how the tree's height changes over time. GeoGebra commands such as slider animation, locus, and graphing are used. Suitable for middle school and above students to learn about exponential growth models.

GeoGebra Commands & Parameters

  1. LaTeX("\text{Identify the known quantities.}") → text2
  2. LaTeX("\text{Identify the unknown quantity or variable.}") → text2_4
  3. LaTeX("\text{Create expressions and equations from the known quantities and variable\textcolor{#000099}{(s)}.}") → text2_6
  4. LaTeX("\text{\textcolor{#000099}{b = 2 }") → text2_9
  5. LaTeX("\text{final value.}") → text2_{14}
  6. LaTeX("\text{\textcolor{#000099}{y = ab^t}") → text2_{16}
  7. LaTeX("\text{Another way to determine the time period is to set up a ratio.}") → text2_{18}
  8. LaTeX("\text{There are \textcolor{#000099}{5} time periods in \textcolor{#000099}{20\; years} since each time period is \textcolor{#000099}{4\; years}.}") → text2_{11}
  9. LaTeX("\text{Follow the order of operations to solve the problem.}") → text2_{19}
  10. LaTeX("\text{Equation from the previous step }") → text2_{23}
  11. LaTeX("\text{Raise \textcolor{#000099}{2} to the fifth power. }") → text2_{24}
  12. LaTeX("\text{Interpret the solution in terms of the context of the problem.}") → text2_{26}
  13. LaTeX((("\text{\textcolor{#000099}{y = " * var1) * "\; •\; 2^5}")) → text2_{20}
  14. LaTeX((("\text{\textcolor{#000099}{y =" * var1) * "\;• \;32}")) → text2_{21}
  15. LaTeX((("\text{Multiply \textcolor{#000099}{" * var1) * "} and \textcolor{#000099}{32}. }")) → text2_{25}
  16. LaTeX((("\text{\textcolor{#000099}{a =" * var1) * "}")) → text2_8
  17. LaTeX((("\text{The initial height of the tree=\textcolor{#000099}{" * var1) * "\; feet.} }")) → text2_1
  18. LaTeX((("\text{\textcolor{#000099}{y = " * var2) * "}")) → text2_{22}
  19. LaTeX("\text{for the base to repeat.}") → text4_3
  20. LaTeX((("\text{\textcolor{#000099}{y = (" * var1) * ")\; •\; (2)^5}")) → text2_{17}
  21. LaTeX("\text{\textcolor{#000099}{x=}every \textcolor{#000099}{4 \;years} for \textcolor{#000099}{20\; years}}") → text2_{10}
  22. LaTeX("\text{\textcolor{#000099}{20\; years\;•\frac{1\;time\;period}{4\;years}=5\;time \;periods} }") → text2_{12}
  23. LaTeX("\text{The amount of time=every \textcolor{#000099}{4\; years} for \textcolor{#000099}{20\; years}.}") → text2_3
  24. LaTeX("\text{Write an exponential equation of the general form \textcolor{#000099}{y=ab^t} and solve the problem.}") → text1_1
  25. LaTeX((("\text{The tree's initial height is \textcolor{#000099}{" * var1) * " \;feet} and its height doubles every \textcolor{#000099}{4\; years}. How tall will it be in \textcolor{#000099}{20\; years}? }")) → text1
  26. LaTeX("\text{The growth rate=doubles, so that means \textcolor{#000099}{2}.}") → text2_2
  27. LaTeX("\text{The unknown quantity is the height of the tree after \textcolor{#000099}{20\; years}. Solve for the final height after \textcolor{#000099}{20\; years}.}") → text2_5
  28. LaTeX("\text{The general form of an exponential equation is \textcolor{#000099}{y = ab^t}, where \textcolor{#000099}{a} is the initial value, \textcolor{#000099}{b} is the base, \textcolor{#000099}{t} is the time, and \textcolor{#000099}{y} is the }") → text2_7
  29. LaTeX("\text{Therefore, \textcolor{#000099}{ x = 5. }") → text2_{13}
  30. LaTeX("\text{Substitute the values into the general exponential formula, \textcolor{#000099}{y = ab^t.}}") → text2_{15}
  31. LaTeX((("\text{In \textcolor{#000099}{20 \;years}, the tree will be \textcolor{#000099}{" * var2) * "\; feet} tall if its height doubles every \textcolor{#000099}{4\; years}.}")) → text2_{27}
  32. LaTeX("\text{\mathbf{exponential\; equation} an equation that has a variable in the exponent; the general }") → text4
  33. LaTeX("\text{form is y=a • b^x, where a is the initial value, b is the base, x is the time, and }") → text4_1
  34. LaTeX("\text{y is the final output value. Another form is y=ab , where t is the time it takes}") → text4_2
  35. LaTeX((("\text{Tree's initial height=" * var1) * " feet}")) → text3