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   "source": [
    "#A helpful script for Exercise 3.4.9, modeling a cooling potato.\n",
    "\n",
    "#The data, in time/temperature pairs:\n",
    "data = [[0, 204], [2, 193], [4, 184], [8, 169], [10, 162], [13, 156], [17, 149], [20, 143], [24, 138], [30, 130]]\n",
    "N = len(data);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#A plot:\n",
    "plt1 = scatter_plot(data);\n",
    "show(plt1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#The temperature might be modeled by the function\n",
    "var('t k');\n",
    "u(t,k) = 72 + 132*exp(-k*t); #The model function to fit\n",
    "SS = function('SS')(k);\n",
    "SS(k) = add((u(data[i][0],k)-data[i][1])^2 for i in range(N));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Now minimize SS(k) with respect to k."
   ]
  }
 ],
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