{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What Does Exponential Growth Look Like?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set(context='talk', palette='deep', color_codes=True, style='darkgrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "time = np.arange(0, 10, 0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fiddle with this rate and see how things change. For large rates, we get the traditional-looking exponential curve. For small rates, things look linear over this small time scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "rate = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.exp(rate * time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x16a74b10c48>]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(time, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}