Calculating a new population - c++

Question

In a population, the birth rate is the percentage increase of the population due to births, and the death rate is the percentage decrease of the population due to deaths. Write a program that asks for the following:
The starting size of a population (minimum 2) (Prompt Enter starting size:)
The annual birth rate (Prompt Enter annual birth rate:)
The annual death rate (Prompt Enter annual death rate:)
The number of years to display (minimum 1) (Prompt Enter years to display:)
The program should then display the starting population and the projected population at the end of each year. It should use a function that calculates and returns the projected new size of the population after a year. The formula is
N = P(1 + B)(1 - D)
where N is the new population size, P is the previous population size, B is the birth rate, and D is the death rate. Annual birth rate and death rate are the typical numbers of births and deaths in a year per 1000 people, expressed as a decimal.
So, for example, if there are normally about 32 births and 26 deaths per 1000 people in a given population, the birth rate would be .032 and the death rate would be .026.
Here is my code; I am having trouble figuring out how to do the calculation.
#include "stdafx.h" // Defines IDE required "pre-compiled" definition files
#include <iomanip>
#include <iostream>
using namespace std
int main ()
{
double startPop, // To hold the starting population.
float birthRate, // To hold the birth rate.
float deathRate; // To hold the death rate.
int numYears; // To hold the number of years to track population changes.
// Input and validate starting population
cout << "This program calculates population change.\n";
cout << "Enter the starting population size: ";
cin >> startPop;
while (startPop < 2.0)
{
cout << "Starting population must be 2 or more. Please re-enter: ";
cin >> startPop;
}
// Input and validate annual birth and death rates
cout << "Enter the annual birth rate (as % of current population): ";
cin >> birthRate;
while (birthRate < 0)
{
cout << "Birth rate percent cannot be negative. Please re-enter: ";
cin >> birthRate;
}
birthRate = birthRate / 100; // Convert from % to decimal.
cout << "Enter the annual death rate (as % of current population): ";
cin >> deathRate;
while (deathRate < 0)
{
cout << "Death rate percent cannot be negative. Please re-enter: ";
cin >> deathRate;
}
deathRate = deathRate / 100; // Convert from % to decimal.
cout << "For how many years do you wish to view population changes? ";
cin >> numYears;
while (numYears < 1)
{
cout << "Years must be one or more. Please re-enter: ";
cin >> numYears;
population = projectedNewSize(populationStartingSize, annualBirthRate, annualDeathRate);
cout << population << endl;
populationStartingSize = population;
}
printPopulations(startPop, birthRate, deathRate, numYears);
return 0;
} // End of main function

Answer 1

You can do this recursively or using a simple for loop.
E.g. Say if the numYears = 10, you would want to loop 10 times.
Create a temporary variable before your for loop and assign it the value of your startPop, e.g. endPop.
Then, starting with an initial population size of endPop, and death rate of deathRate as well as birth rate of birthRate, you calculate the population size after one year.
Having computed the population after one year in the first loop, you update endPop with the new value.
Subsequently, in the second loop, you use endPop once again as the new starting population size and the cycle repeats itself up till the end of your for loop, i.e. when 10 years have passed.
You did not declare the variable population in the above code snippet before using it.
Implementation:
while (numYears < 1)
{
cout << "Years must be one or more. Please re-enter: ";
cin >> numYears;
}
double population = populationStartingSize;
for ( int i = 0; i < numYears; i++) {
population = projectedNewSize(population, annualBirthRate, annualDeathRate);
cout << "After " << i+1 << "years: " << population << endl;
}
}
Take note that there is chance of over- and under-flow if your number gets too small or too big.
Implementation:
double projectedNewSize(double populationStartingSize, float annualBirthRate, float annualDeathRate) {
return populationStartingSize * (1 + annualBirthRate) * (1 - annualDeathRate);
}
For reading of numYears, you could consider using a do-while loop, :p.