add explanation

Colombia/bonus.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -25,7 +25,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -35,7 +35,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
@@ -139,7 +139,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -156,7 +156,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -165,7 +165,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
@@ -190,7 +190,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
@@ -294,7 +294,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
@@ -334,7 +334,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -343,7 +343,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -355,7 +355,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
@@ -407,7 +407,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -418,7 +418,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -432,7 +432,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Geometric gradient - exponential method"
+    "## Geometric gradient - exponential method\n",
+    "\n",
+    "$$ \\frac{2}{3} $$"
    ]
   },
   {
@@ -455,7 +457,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -466,7 +468,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
@@ -486,7 +488,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -505,7 +507,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -538,7 +540,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {

main.py

@@ -117,6 +117,30 @@
 
 # Geometric gradient (exponential method)
 st.subheader('Geometric gradient (exponential method)')
+st.write('''
+Gradient growth, often referred to as exponential growth, signifies a pattern where the rate of increase of a quantity is proportional to its current value. In simple terms, it's growth at a compounding or accelerating rate, where the larger the current value, the faster it grows over time.
+
+Unlike linear growth, where the increase is constant and steady, gradient growth demonstrates an accelerating or decelerating rate of change. When plotted on a graph, this type of growth results in a curve that steepens or flattens out, showcasing rapid expansion over time.
+
+Mathematically, gradient growth can be represented by an exponential function, often in the form of  $ y = a * b^x $,  where:
+         
+- y represents the final value or quantity,
+
+- a is the initial value or quantity,
+
+- b is the growth factor or rate,
+
+- x is time or the number of periods.
+         
+''')
+
+left_co, cent_co, last_co = st.columns(3)
+
+with cent_co: 
+    st.image(
+        'https://ccp.ucr.ac.cr/cursos/demografia_03/Imagenes/quinta12.gif',
+        caption='Interpolation linear',
+    )
 
 
 df_gradient = Gradient.calcule(
@@ -140,6 +164,32 @@
 
 # Geometric gradient (exponential method)
 st.subheader('Logistic method')
+st.write('''
+Logistic growth represents a type of growth pattern where a population or a quantity initially experiences exponential or rapid growth, but eventually reaches a point where growth slows down and stabilizes. This pattern is often described as an S-shaped curve.
+
+In logistic growth, the population or quantity starts with a period of rapid increase when resources are abundant. However, as the population approaches a certain limit or carrying capacity - the maximum population size that the environment can sustain - the growth rate gradually slows down. Eventually, the population stabilizes near the carrying capacity, resulting in a relatively constant population size.
+         
+
+
+
+         
+Mathematically, logistic growth is described using the logistic equation, which can be represented as:
+
+$$ P(t) = \\frac {K}{1 + e^{-r * t}} $$
+ 
+Where:
+
+- P(t) represents the population (or quantity) at time.
+
+- K is the carrying capacity or the maximum population size the environment can sustain.
+
+- r is the growth rate of the population.
+
+- e is the base of the natural logarithm.
+
+- t is time.
+         
+''')
 
 
 df_logistic = Logistic.calcule(

methods/logistic.py

@@ -18,14 +18,19 @@ def calcule(
                 populations: A numpy array with the populations data
                 years: A numpy array with the years data
         '''
-        def modelo_logistic(t, M, k, c):
+        def modelo_logistic(t, M, k, c, A):
             '''
                 Schema for the model logistic
             '''
-            return M / (1 + k * np.exp(-c * t))
+            return M / (1 + k * np.exp(-c * t)) + A
 
 
-        popt, pcov = curve_fit(modelo_logistic, years, populations)
+        popt, pcov = curve_fit(
+            modelo_logistic, 
+            years, 
+            populations,
+        )
+        print(popt)
 
         new_population = modelo_logistic(data_predicted, *popt)