{
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   "source": [
    "> **This is a saved, working copy.** Sliders here are frozen at their\n",
    "> starting value — there's no marimo runtime in plain Jupyter to drive them.\n",
    "> For the live, drag-the-sliders version of this lab, see\n",
    "> [Week 1 lab — interactive](https://math4120.pages.dev/wasm/week01_lab.html).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ipython-import",
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   "outputs": [],
   "source": [
    "from IPython.display import Markdown, HTML\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hbol",
   "metadata": {
    "marimo": {
     "config": {
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   "source": [
    "# Week 1 lab: your first models\n",
    "\n",
    "**MATH4120 — Mathematical Modelling and Programming** Lancaster University, 2026–27\n",
    "\n",
    "---\n",
    "\n",
    "New to Marimo, or not sure how it relates to Jupyter (which you'll use to save and submit your work)? See the [Getting Started guide](https://math4120.pages.dev/getting-started/marimo.html) first — it's a two-minute read and explains how the two fit together.\n",
    "\n",
    "This notebook has two kinds of cell:\n",
    "\n",
    "- **Text cells** (like this one) contain explanations and tasks written in Markdown. Double-click any text cell to edit it; press **Ctrl+Enter** to render.\n",
    "- **Code cells** (grey background) contain Python.  Press **Ctrl+Enter** (or **Shift+Enter**) to run a cell and see its output immediately below.\n",
    "\n",
    "When a code cell has a placeholder value (`0.0` or `np.zeros_like(...)`), replace it with the correct expression and run the cell.  Everything that depends on your result will update automatically.\n",
    "\n",
    "Errors are normal — read the message, fix the line, run again.  Ask a demonstrator if you are stuck for more than a few minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "MJUe",
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vblA",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
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   "source": [
    "## Exercise 0 — writing in Markdown\n",
    "\n",
    "Text cells use **Markdown**: a lightweight way to write formatted text and maths. The maths notation is **LaTeX** — the same as in the printed lecture notes.\n",
    "\n",
    "| What you type | What you see |\n",
    "|---|---|\n",
    "| `**bold**` | **bold** |\n",
    "| `*italic*` | *italic* |\n",
    "| `## Heading` | a section heading |\n",
    "| `$N_{n+1}$` | $N_{n+1}$ (subscript) |\n",
    "| `$e^{rt}$` | $e^{rt}$ (superscript) |\n",
    "| `$\\frac{dN}{dt}$` | $\\frac{dN}{dt}$ (fraction) |\n",
    "| `$\\alpha,\\,\\beta,\\,\\theta$` | $\\alpha,\\,\\beta,\\,\\theta$ (Greek letters) |\n",
    "| `$$N_{n+1} = R\\,N_n$$` | a centred display equation on its own line |\n",
    "\n",
    "**Task.** Double-click the cell below and fill in:\n",
    "1. A `##` heading with your name.\n",
    "2. The geometric growth rule $N_{n+1} = R\\,N_n$ as a display equation (`$$...$$`).\n",
    "3. One sentence in **bold** describing what you hope to get out of today.\n",
    "\n",
    "Press **Ctrl+Enter** to render it.\n",
    "\n",
    "(Same syntax works in Jupyter later — there's a quick-reference table in the [Getting Started guide](https://math4120.pages.dev/getting-started/jupyter.html#markdown-basics) if you ever need a reminder.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bkHC",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
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   },
   "source": [
    "## Your name here\n",
    "\n",
    "$$N_{n+1} = ???$$\n",
    "\n",
    "**Write one sentence here in bold.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lEQa",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
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   "source": [
    "## The tools: NumPy and Matplotlib\n",
    "\n",
    "The first code cell imports two libraries:\n",
    "\n",
    "```python\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "```\n",
    "\n",
    "Think of them as toolboxes.  **NumPy** (`np`) provides arrays and mathematical functions; **Matplotlib** (`plt`) produces plots.\n",
    "\n",
    "The key idea in NumPy is that operations work on **whole arrays at once**. If `t` is an array of 200 time values, then `np.exp(r * t)` computes $e^{rt}$ at all 200 points simultaneously — no loop needed.  This is called *vectorisation* and is why scientific Python code rarely has explicit loops over data.\n",
    "\n",
    "Functions you will use today:\n",
    "\n",
    "| Call | What it does |\n",
    "|---|---|\n",
    "| `np.linspace(a, b, n)` | $n$ evenly spaced values from $a$ to $b$ |\n",
    "| `np.arange(n)` | integers $0, 1, \\ldots, n-1$ |\n",
    "| `np.zeros(n)` | array of $n$ zeros (used to pre-allocate before a loop) |\n",
    "| `np.exp(x)` | $e^x$, element-wise if `x` is an array |\n",
    "| `np.log(x)` | natural logarithm, element-wise |\n",
    "\n",
    "**Looking up documentation.**  Run `help(np.linspace)` in any code cell to read the full documentation for a function.  Try replacing `np.linspace` with `np.zeros` or `np.exp` to look those up too."
   ]
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     "text": [
      "Help on _ArrayFunctionDispatcher in module numpy:\n",
      "\n",
      "linspace(\n",
      "    start,\n",
      "    stop,\n",
      "    num=50,\n",
      "    endpoint=True,\n",
      "    retstep=False,\n",
      "    dtype=None,\n",
      "    axis=0,\n",
      "    *,\n",
      "    device=None\n",
      ")\n",
      "    Return evenly spaced numbers over a specified interval.\n",
      "\n",
      "    Returns `num` evenly spaced samples, calculated over the\n",
      "    interval [`start`, `stop`].\n",
      "\n",
      "    The endpoint of the interval can optionally be excluded.\n",
      "\n",
      "    .. versionchanged:: 1.20.0\n",
      "        Values are rounded towards ``-inf`` instead of ``0`` when an\n",
      "        integer ``dtype`` is specified. The old behavior can\n",
      "        still be obtained with ``np.linspace(start, stop, num).astype(np.int_)``\n",
      "\n",
      "    Parameters\n",
      "    ----------\n",
      "    start : array_like\n",
      "        The starting value of the sequence.\n",
      "    stop : array_like\n",
      "        The end value of the sequence, unless `endpoint` is set to False.\n",
      "        In that case, the sequence consists of all but the last of ``num + 1``\n",
      "        evenly spaced samples, so that `stop` is excluded.  Note that the step\n",
      "        size changes when `endpoint` is False.\n",
      "    num : int, optional\n",
      "        Number of samples to generate. Default is 50. Must be non-negative.\n",
      "    endpoint : bool, optional\n",
      "        If True, `stop` is the last sample. Otherwise, it is not included.\n",
      "        Default is True.\n",
      "    retstep : bool, optional\n",
      "        If True, return (`samples`, `step`), where `step` is the spacing\n",
      "        between samples.\n",
      "    dtype : dtype, optional\n",
      "        The type of the output array.  If `dtype` is not given, the data type\n",
      "        is inferred from `start` and `stop`. The inferred dtype will never be\n",
      "        an integer; `float` is chosen even if the arguments would produce an\n",
      "        array of integers.\n",
      "    axis : int, optional\n",
      "        The axis in the result to store the samples.  Relevant only if start\n",
      "        or stop are array-like.  By default (0), the samples will be along a\n",
      "        new axis inserted at the beginning. Use -1 to get an axis at the end.\n",
      "    device : str, optional\n",
      "        The device on which to place the created array. Default: None.\n",
      "        For Array-API interoperability only, so must be ``\"cpu\"`` if passed.\n",
      "\n",
      "        .. versionadded:: 2.0.0\n",
      "\n",
      "    Returns\n",
      "    -------\n",
      "    samples : ndarray\n",
      "        There are `num` equally spaced samples in the closed interval\n",
      "        ``[start, stop]`` or the half-open interval ``[start, stop)``\n",
      "        (depending on whether `endpoint` is True or False).\n",
      "    step : float, optional\n",
      "        Only returned if `retstep` is True\n",
      "\n",
      "        Size of spacing between samples.\n",
      "\n",
      "\n",
      "    See Also\n",
      "    --------\n",
      "    arange : Similar to `linspace`, but uses a step size (instead of the\n",
      "             number of samples).\n",
      "    geomspace : Similar to `linspace`, but with numbers spaced evenly on a log\n",
      "                scale (a geometric progression).\n",
      "    logspace : Similar to `geomspace`, but with the end points specified as\n",
      "               logarithms.\n",
      "    :ref:`how-to-partition`\n",
      "\n",
      "    Examples\n",
      "    --------\n",
      "    >>> import numpy as np\n",
      "    >>> np.linspace(2.0, 3.0, num=5)\n",
      "    array([2.  , 2.25, 2.5 , 2.75, 3.  ])\n",
      "    >>> np.linspace(2.0, 3.0, num=5, endpoint=False)\n",
      "    array([2. ,  2.2,  2.4,  2.6,  2.8])\n",
      "    >>> np.linspace(2.0, 3.0, num=5, retstep=True)\n",
      "    (array([2.  ,  2.25,  2.5 ,  2.75,  3.  ]), 0.25)\n",
      "\n",
      "    Graphical illustration:\n",
      "\n",
      "    >>> import matplotlib.pyplot as plt\n",
      "    >>> N = 8\n",
      "    >>> y = np.zeros(N)\n",
      "    >>> x1 = np.linspace(0, 10, N, endpoint=True)\n",
      "    >>> x2 = np.linspace(0, 10, N, endpoint=False)\n",
      "    >>> plt.plot(x1, y, 'o')\n",
      "    [<matplotlib.lines.Line2D object at 0x...>]\n",
      "    >>> plt.plot(x2, y + 0.5, 'o')\n",
      "    [<matplotlib.lines.Line2D object at 0x...>]\n",
      "    >>> plt.ylim([-0.5, 1])\n",
      "    (-0.5, 1)\n",
      "    >>> plt.show()\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(np.linspace)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Xref",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
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     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 1 — plotting an exponential\n",
    "\n",
    "The exponential model $N(t) = N_0\\,e^{rt}$ describes a population growing (or decaying) at a constant per-capita rate $r$.\n",
    "\n",
    "The cell below is already complete — run it first to see what it produces.\n",
    "\n",
    "1. Change $r$ to $-0.3$ and run again.  What changes?\n",
    "2. Change $N_0$ to $500$ and run again.\n",
    "3. What value of $r$ keeps the population exactly constant?"
   ]
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    {
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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N0 = 100\n",
    "r = 0.3\n",
    "\n",
    "t = np.linspace(0, 10, 200)\n",
    "N = N0 * np.exp(r * t)\n",
    "\n",
    "fig1, ax1 = plt.subplots(figsize=(7, 4))\n",
    "ax1.plot(t, N, color=\"#1a5276\", linewidth=2)\n",
    "ax1.set_xlabel(\"Time $t$\")\n",
    "ax1.set_ylabel(\"Population $N(t)$\")\n",
    "ax1.set_title(\"Exponential model\")\n",
    "ax1.grid(True, alpha=0.3)\n",
    "fig1;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "BYtC",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 2 — iterating a difference equation\n",
    "\n",
    "Instead of a closed formula, we can build a sequence step by step.  The geometric growth rule is $$N_{n+1} = R\\,N_n.$$\n",
    "\n",
    "The code below sets up an array and fills it in with a `for` loop.  One line is missing.\n",
    "\n",
    "**Task.**\n",
    "1. Replace `0.0` on the marked line with the iteration rule.  Use `R` and `N_d[n]`.\n",
    "2. Run the cell.  The plot below will update automatically.\n",
    "3. Try `R = 0.7`, then `R = 1.0`, then `R = 2.5`.  Describe what you observe each time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "RGSE",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:30.046785Z",
     "iopub.status.busy": "2026-11-13T23:25:30.046595Z",
     "iopub.status.idle": "2026-11-13T23:25:30.051641Z",
     "shell.execute_reply": "2026-11-13T23:25:30.050745Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([100.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,\n",
       "         0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.,   0.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R = 1.35      # try 0.7, 1.0, 2.5\n",
    "N0_d = 100\n",
    "steps = 20\n",
    "\n",
    "N_d = np.zeros(steps + 1)\n",
    "N_d[0] = N0_d\n",
    "for n in range(steps):\n",
    "    N_d[n + 1] = 0.0   # ← replace 0.0 with R * N_d[n]\n",
    "N_d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "Kclp",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:30.053317Z",
     "iopub.status.busy": "2026-11-13T23:25:30.053158Z",
     "iopub.status.idle": "2026-11-13T23:25:30.180467Z",
     "shell.execute_reply": "2026-11-13T23:25:30.179456Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig2, _ax2 = plt.subplots(figsize=(7, 4))\n",
    "_ax2.stem(np.arange(steps + 1), N_d, linefmt=\"#1a5276\", markerfmt=\"C0o\", basefmt=\"k-\")\n",
    "_ax2.set_xlabel(\"Generation $n$\")\n",
    "_ax2.set_ylabel(\"Population\")\n",
    "_ax2.set_title(f\"Geometric growth  ($R = {R}$)\")\n",
    "_ax2.grid(True, alpha=0.3)\n",
    "_fig2;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "emfo",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Exercise 3 — the logistic map\n",
    "\n",
    "The geometric model grows without bound when $R > 1$.  A carrying capacity $K$ adds a braking factor: $$N_{n+1} = R\\,N_n\\!\\left(1 - \\frac{N_n}{K}\\right).$$\n",
    "\n",
    "When $N_n \\ll K$ this behaves like geometric growth.  When $N_n$ approaches $K$ the factor $(1 - N_n/K)$ suppresses growth.\n",
    "\n",
    "**Task.**\n",
    "1. Replace `0.0` on the marked line with the logistic rule. Use `R_log`, `N_log[n_log]`, and `K`.\n",
    "2. Run for `R_log = 2.0`.  Describe the long-term behaviour.\n",
    "3. Change `R_log` to `3.2`, then `3.8`.  What happens?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "Hstk",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:30.182481Z",
     "iopub.status.busy": "2026-11-13T23:25:30.182301Z",
     "iopub.status.idle": "2026-11-13T23:25:30.187039Z",
     "shell.execute_reply": "2026-11-13T23:25:30.186133Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "        0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "        0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "        0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "        0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_log = 2.0    # try 3.2, then 3.8\n",
    "K = 100\n",
    "N0_log = 10\n",
    "steps_log = 60\n",
    "\n",
    "N_log = np.zeros(steps_log + 1)\n",
    "N_log[0] = N0_log\n",
    "for n_log in range(steps_log):\n",
    "    N_log[n_log + 1] = 0.0   # ← replace 0.0 with the logistic rule\n",
    "N_log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "nWHF",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:30.188783Z",
     "iopub.status.busy": "2026-11-13T23:25:30.188583Z",
     "iopub.status.idle": "2026-11-13T23:25:30.352126Z",
     "shell.execute_reply": "2026-11-13T23:25:30.351167Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig3, _ax3 = plt.subplots(figsize=(8, 4))\n",
    "_ax3.stem(np.arange(steps_log + 1), N_log, linefmt=\"#1a5276\", markerfmt=\"C0.\", basefmt=\"k-\")\n",
    "_ax3.axhline(K, color=\"grey\", linestyle=\"--\", alpha=0.5, label=f\"$K = {K}$\")\n",
    "_ax3.set_xlabel(\"Year $n$\")\n",
    "_ax3.set_ylabel(\"Population\")\n",
    "_ax3.set_title(f\"Logistic map  ($R = {R_log}$,  $K = {K}$)\")\n",
    "_ax3.legend()\n",
    "_ax3.grid(True, alpha=0.3)\n",
    "_fig3;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "iLit",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "**Your observations** (double-click to edit this cell):\n",
    "\n",
    "- $R = 2.0$: *write one sentence here*\n",
    "- $R = 3.2$: *write one sentence here*\n",
    "- $R = 3.8$: *write one sentence here*"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ZHCJ",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Extension — Newton's law of cooling\n",
    "\n",
    "A cup of coffee starts at $90°$C in a room at $20°$C.  Newton's law of cooling gives the temperature at time $t$ (minutes): $$T(t) = T_\\infty + (T_0 - T_\\infty)\\,e^{-kt}.$$\n",
    "\n",
    "**Task.**\n",
    "1. Replace `np.zeros_like(t_cool)` with the formula for $T(t)$. Use `T0_cool`, `Tinf_cool`, `k_cool`, `t_cool`, and `np.exp(...)`.\n",
    "2. Run the cell.  At roughly what time does the coffee reach $60°$C?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ROlb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:30.354267Z",
     "iopub.status.busy": "2026-11-13T23:25:30.354061Z",
     "iopub.status.idle": "2026-11-13T23:25:30.356979Z",
     "shell.execute_reply": "2026-11-13T23:25:30.356227Z"
    }
   },
   "outputs": [],
   "source": [
    "T0_cool   = 90.0   # initial temperature (°C)\n",
    "Tinf_cool = 20.0   # room temperature (°C)\n",
    "k_cool    = 0.05   # cooling rate (min⁻¹)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "qnkX",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:30.359249Z",
     "iopub.status.busy": "2026-11-13T23:25:30.359025Z",
     "iopub.status.idle": "2026-11-13T23:25:30.369137Z",
     "shell.execute_reply": "2026-11-13T23:25:30.368437Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "       0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_cool = np.linspace(0, 60, 300)\n",
    "T_cool = np.zeros_like(t_cool)   # ← replace with the formula\n",
    "T_cool"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "TqIu",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:30.370802Z",
     "iopub.status.busy": "2026-11-13T23:25:30.370631Z",
     "iopub.status.idle": "2026-11-13T23:25:30.517555Z",
     "shell.execute_reply": "2026-11-13T23:25:30.516543Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig4, _ax4 = plt.subplots(figsize=(7, 4))\n",
    "_ax4.plot(t_cool, T_cool, color=\"#1a5276\", linewidth=2)\n",
    "_ax4.axhline(Tinf_cool, color=\"grey\", linestyle=\"--\", alpha=0.6,\n",
    "             label=f\"Room temperature {Tinf_cool}°C\")\n",
    "_ax4.set_xlabel(\"Time (min)\")\n",
    "_ax4.set_ylabel(\"Temperature (°C)\")\n",
    "_ax4.set_title(f\"Newton's law of cooling  ($k = {k_cool}$ min⁻¹,  $T_0 = {T0_cool}$°C)\")\n",
    "_ax4.legend()\n",
    "_ax4.grid(True, alpha=0.3)\n",
    "_fig4;"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.3"
  },
  "marimo": {
   "app_config": {
    "app_title": "Week 1 Lab — Your first models",
    "width": "medium"
   },
   "marimo_version": "0.25.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}