Exp-growth.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Which exponential grows faster?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "X = np.linspace(-5, 4, 100)\n",
    "ax.plot(X, np.exp(X), label='$e^x$')\n",
    "ax.plot(X, np.exp(2*X)+np.exp(X), label='$e^{2x}+e^x$')\n",
    "ax.plot(X, np.exp(2*X)-np.exp(X), label='$e^{2x}-e^x$')\n",
    "ax.plot(X, np.exp(2*X)-20*np.exp(X), label='$e^{2x}-20e^x$')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "X = np.linspace(0, 5, 100)\n",
    "ax.plot(X, np.exp(X), label='$e^x$')\n",
    "ax.plot(X, np.exp(2*X), label='$e^{2x}$')\n",
    "ax.plot(X, np.exp(2*X)-20*np.exp(X), label='$e^{2x}-20e^x$')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "X = np.linspace(-5, 7, 100)\n",
    "ax.plot(X, np.exp(X), label='$e^x$')\n",
    "ax.plot(X, -np.exp(X), label='$-e^x$')\n",
    "ax.plot(X, np.exp(X) * np.cos(3*X), label='$e^x\\cos 3x$')\n",
    "ax.legend()"
   ]
  }
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