Answer:
// using c++ language
#include "stdafx.h";
#include <iostream>
#include<cmath>
using namespace std;
//start
int main()
{
  //Declaration of variables in the program
  double start_organisms;
  double daily_increase;
  int days;
  double updated_organisms;
  //The user enters the number of organisms as desired
  cout << "Enter the starting number of organisms: ";
  cin >> start_organisms;
  //Validating input data
  while (start_organisms < 2)
  {
      cout << "The starting number of organisms must be at least 2.\n";
      cout << "Enter the starting number of organisms: ";
      cin >> start_organisms;
  }
  //The user enters daily input, here's where we apply the 5.2% given in question
  cout << "Enter the daily population increase: ";
  cin>> daily_increase;
  //Validating the increase
  while (daily_increase < 0)
  {
      cout << "The average daily population increase must be a positive value.\n ";
      cout << "Enter the daily population increase: ";
      cin >> daily_increase;
  }
  //The user enters number of days
  cout << "Enter the number of days: ";
  cin >> days;
  //Validating the number of days
  while (days<1)
  {
      cout << "The number of days must be at least 1.\n";
      cout << "Enter the number of days: ";
      cin >> days;
  }
  
  //Final calculation and display of results based on formulas
  for (int i = 0; i < days; i++)
  {
      updated_organisms = start_organisms + (daily_increase*start_organisms);
      cout << "On day " << i + 1 << " the population size was " << round(updated_organisms)<<"."<<"\n";
      
      start_organisms = updated_organisms;
  }
  system("pause");
   return 0;
//end
}
Explanation: