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t1_Model_P_and_dP_dt.ipynb

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+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "name": "t1: Model P and dP/dt",
+      "provenance": [],
+      "authorship_tag": "ABX9TyMvCiGfC2ZmhxzJaPasVAy5",
+      "include_colab_link": true
+    },
+    "kernelspec": {
+      "name": "python3",
+      "display_name": "Python 3"
+    },
+    "language_info": {
+      "name": "python"
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "<a href=\"https://colab.research.google.com/github/awangberg/AdvLinearAlgebra/blob/master/t1_Model_P_and_dP_dt.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 696
+        },
+        "id": "IgWpD6JTjVCN",
+        "outputId": "049e090f-2e0b-49d4-d203-d7b4564d843d"
+      },
+      "source": [
+        "from IPython.display import IFrame\n",
+        "IFrame(src=\"https://www.desmos.com/calculator/vu2oojhtvx\", width=1500, height=675)"
+      ],
+      "execution_count": 3,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/html": [
+              "\n",
+              "        <iframe\n",
+              "            width=\"1500\"\n",
+              "            height=\"675\"\n",
+              "            src=\"https://www.desmos.com/calculator/vu2oojhtvx\"\n",
+              "            frameborder=\"0\"\n",
+              "            allowfullscreen\n",
+              "        ></iframe>\n",
+              "        "
+            ],
+            "text/plain": [
+              "<IPython.lib.display.IFrame at 0x7faff81b9a10>"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 3
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "jVXZ4oDPjY20"
+      },
+      "source": [
+        "# The production (in tons) of apples is given in the table above.\n",
+        "\n",
+        "\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "UCZjqlqlrOQo"
+      },
+      "source": [
+        "## Units:  Describe the quantities (with units!) for the quantities:\n",
+        "\n",
+        "   * P  :  tons\n",
+        "   * t  :  _____\n",
+        "   * dP :  _____\n",
+        "   * dt :  _____\n",
+        "   * dP/dt : _____"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "DDqVQT9YodrO"
+      },
+      "source": [
+        "##  Behavior of P  [ include units! ]\n",
+        "\n",
+        "*  What is the maximum amount of apples produced during the 4 years?\n",
+        "\n",
+        "*  What is the minimum amount of apples produced during the 4 years?\n",
+        "\n",
+        "*  How long does it take the production to repeat itself?"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "OIf-D8LAor5q"
+      },
+      "source": [
+        "## Behavior of $\\frac{dP}{dt}$  [ include units! ]\n",
+        "\n",
+        "Add a column to the table in Desmos showing $\\frac{dP}{dt}$.  [ Enter \"d_P / d_t \" ]\n",
+        "\n",
+        "* What is the maximum value of $\\frac{dP}{dt}$ during the 4 years?\n",
+        "\n",
+        "* What is the minimum value of $\\frac{dP}{dt}$ during the 4 years?\n",
+        "\n",
+        "* How long does it take $\\frac{dP}{dt}$ to repeat itself?"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "k8ffkZX3kr2R"
+      },
+      "source": [
+        "# Selecting Models \n",
+        "\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "bC8xookVqypu"
+      },
+      "source": [
+        "## Production Model\n",
+        "\n",
+        "What type of functions would be appropriate to model the production data?  Provide a one-sentence justification for choosing appropriate models, or for dismissing the models.\n",
+        "\n",
+        "* linear functions:\n",
+        "\n",
+        "* quadratic functions:\n",
+        "\n",
+        "* exponential functions:\n",
+        "\n",
+        "* logarithmic functions:\n",
+        "\n",
+        "* sine functions:\n",
+        "\n",
+        "* cosine functions:\n",
+        "\n",
+        "* quotient of two functions:\n",
+        "\n",
+        "#  Model of how Production changes, $\\frac{dP}{dt}$\n",
+        "\n",
+        "What type of functions would be appropriate to model how the rate of change of the production data,  $dP/dt$? Provide a one-sentence justification for choosing appropriate models, or for dismissing the models.\n",
+        "\n",
+        "* linear functions:\n",
+        "\n",
+        "* quadratic functions:\n",
+        "\n",
+        "* exponential functions:\n",
+        "\n",
+        "* logarithmic functions:\n",
+        "\n",
+        "* sine functions:\n",
+        "\n",
+        "* cosine functions:\n",
+        "\n",
+        "* quotient of two functions:\n",
+        "\n",
+        "\n",
+        "\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "04jbqX3llRsb"
+      },
+      "source": [
+        "#  Using Desmos, find the best fit function for:\n",
+        "\n",
+        "  *  The production data $P$:\n",
+        "\n",
+        "    $P = $ [ Enter your answer here ]\n",
+        "\n",
+        "  *  The data for $\\frac{dP}{dt}$:\n",
+        "  \n",
+        "    $\\frac{dP}{dt} = $ [ Enter your answer here ]\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "CQIMw7URnaL8"
+      },
+      "source": [
+        "#  End of the worksheet....\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "INxMv4a7mdWk"
+      },
+      "source": [
+        "Note:  The table was generated from a Google Sheets worksheet, and just pasted into the Desmos activity.\n",
+        "\n",
+        "https://docs.google.com/spreadsheets/d/1HJIghAaJNqG6zc912Plrc_R6muKavRPhOWuMpR49sfg/edit?usp=sharing"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "9qyDkW7Gjpin"
+      },
+      "source": [
+        ""
+      ],
+      "execution_count": null,
+      "outputs": []
+    }
+  ]
+}