Project_2_Related_Rates_and_Linear_Approximation.ipynb

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      "name": "Project 2:  Related Rates and Linear Approximation.ipynb",
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      "name": "python"
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      "source": [
        "#Project 2:  Linear Approximation, Related Rates, Optimization\n",
        "\n",
        "For this project, you will solve the following two problems:\n",
        "\n",
        "  1.  Create linear and higher-order approximations for $y = ln(x)$.  Your models will be used to create various estimates of $y = ln(1+a)$.  You'll also make a guess a the actual value of $ln(1+a)$ based on your improvements in the estimate.\n",
        "\n",
        "  2.  Solve a related rates problem both algebraically and computationally.  You'll then adjust one of the quantities to see the impact on your results.  When working on this project, your results should be consistent with each other.\n",
        "\n",
        "One final question will be related to your preferences for using computation or algebra for solving problems.  Be sure to provide concrete examples of when you prefer to solve a problem algebraically or computationally.\n"
      ],
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      "source": [
        "# Project 2A:  Approximate $y = ln(x)$ near $x = 1$\n",
        "\n",
        "In this project, you will approximate the function\n",
        "\n",
        "$$  y = ln(x) $$\n",
        "\n",
        "using the best point, line, parabola, and third-degree polynomial.  The code is written in Desmos.  You'll be asked to provide a screenshot showing:\n",
        "\n",
        "  1.  The approximation with just a contant\n",
        "  2.  The approximation with just a line (using a derivative)\n",
        "  3.  The approximation with a quadratic (using 1st and 2nd derivatives)\n",
        "  4.  The approximation with a cubic (using 1st, 2nd, and 3rd derivatives)\n",
        "\n",
        "For this project, You'll also develop three methods for approximating \n",
        "\n",
        "$$  ln(1+a) $$\n",
        "\n",
        "for both positive and negative values of $a$ near 0."
      ],
      "metadata": {
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    {
      "cell_type": "code",
      "source": [
        "desmosSheet1 = \"https://www.desmos.com/calculator/phmfcgjnhh\"\n",
        "#  Copy the url above and paste into a separate browser window.\n",
        "#  Then, make screen captures and paste the results into the cells below.\n",
        "#  Uncomment these to put the Desmos page here:\n",
        "#from IPython.display import IFrame\n",
        "#IFrame(src=desmosSheet1, width=1200, height=575)"
      ],
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      "source": [
        "## A - 1  Approximating the curve with just a constant:\n",
        "\n",
        "The approximation to $y = ln(x)$ is given by\n",
        "\n",
        "$$  y \\approx ln(0) $$\n"
      ],
      "metadata": {
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)"
      ],
      "metadata": {
        "id": "FAPWxaFnVxzg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## A - 2  Approximating the curve with just a line (using a derivative):"
      ],
      "metadata": {
        "id": "3hl7h2lbLCU_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<< Paste the image from Desmos here >>"
      ],
      "metadata": {
        "id": "XbbWcZQBV3ox"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## A - 3  Approximating the curve with a quadratic (using a 1st and 2nd derivative):"
      ],
      "metadata": {
        "id": "Qp-TcqLBLRbh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "<< Paste the image from Desmos here. >>"
      ],
      "metadata": {
        "id": "Pe4mlfjjV7Em"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Project 2B:  Related Rates problem\n",
        "\n",
        "In this project, you will determine the rate at which the water level is rising in a swimming pool.  You'll be asked to solve the problem both symbolically, using algebra, and computationally, using Sheets, Desmos, and Colab.  Your answers should agree.  At the end of the project, you'll discuss the advantage or disadvantage of each approach.\n",
        "\n",
        "## Problem: Related Rates ##\n",
        "\n",
        "A rectangular swimming pool $15$ meters long and $8$ meters wide has a depth of $4$ meters at one end and $0.5$ meters at the other end.  On a bright sunny day, the water level is initially $3$ meters deep at the deep end.  An average college student has a volume of $84$ liters.  If the college students jump into the pool at a rate of one every $15 sec$, how quickly is the water level rising when the 6th college student enters the pool?\n",
        "\n",
        "[Note:   Assume that students stay in the pool and keep their heads, which have a volume of $9 $ liters, above water! ]\n",
        "\n",
        "[ Note 2:  $1$ liter is the same as $0.001$ cubic meters ]\n",
        "\n",
        "Part 1:  Determine the original volume of water in the pool.  Give the result in both Liters and cubic meters.\n",
        "\n",
        "Part 2:  Find an equation between the height of the water in the pool and the volume ( of water and bodies) in the pool.\n",
        "\n",
        "Part 3:  Solve the problem algebraically.  Your solution should include differentials, derivatives, and the appropriate evaluation.\n",
        "\n",
        "Part 4:  Create a table capturing the time, number of students and water in the pool, and the height of the water in the pool at a given time:\n",
        "\n",
        "  | time | # of students in pool |   Volume  | Water level |\n",
        "  |------|-----------------------|-----------|------------|\n",
        "  | 0 sec |        0             |     ??    |    3 m     |\n",
        "  | 15 sec|        1             |  ?? + 75  |     ??     |\n",
        "  |       |        2             |           |            |\n",
        "  |       |        3             |           |            |\n",
        "  |       |        4             |           |            |\n",
        "  |       |        5             |           |            |\n",
        "  |       |        6             |           |            |\n",
        "  |       |        7             |           |            |\n",
        "  \n",
        "Part 5:  Using your table, find the rate at which the water level is rising in meters per student.\n",
        "\n",
        "Part 6:  Water evaporation is fairly insignificant, losing about $0.25$ liters per minute.  Include this information into either your algebraic or computation solution.  What is the overall impact on the rate at which water is rising (in meters per student)?\n",
        "\n",
        "\n",
        "If you use Desmos or Colab for any of your work, be sure to take a screen shot and paste it into this Colab project below.  Write your answers and algebraic work in the packet.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "QooktVveGuoZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "cI76VgWxQhS_"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bVnNOc5SZDa7"
      },
      "source": [
        "# If you would like to use a Google Sheet, create one and paste the url into the cell below.\n",
        "GoogleSheet_URL = \"\"\n",
        "#from IPython.display import IFrame\n",
        "#IFrame(src=GoogleSheet_URL, width=800, height=375)"
      ],
      "execution_count": 2,
      "outputs": []
    }
  ]
}