Programming Exercises

1. (Population projection) The U.S. Census Bureau projects population based on the
following assumptions:
■ One birth every 7 seconds
■ One death every 13 seconds
■ One new immigrant every 45 seconds
Write a program to display the population for each of the next five years. Assume the
current population is 312,032,486 and one year has 365 days. 
Hint: In Java, if two integers perform division, the result is an integer. The fractional part is truncated. 
For example, 5 / 4 is 1 (not 1.25) and 10 / 4 is 2 (not 2.5). To get an accurate result with the fractional part, one of the values involved in the division must be a number with a decimal point. For example, 5.0 / 4 is 1.25 and 10 / 4.0 is 2.5.

Program Code: 
//Population.java
public class Population
{//Main method 

  public static void main(String[] args) 
        {
        //Declare current population as variable population 
        double population = 312032486;

    //add one birth every 7 seconds; subtract one

    //death              

    //add one birth every 7 seconds; subtract one

    //death every 13 seconds; add one immigrant  

    //every 45 seconds.

        //365 days = 1 year | 1 day = 24 hours | 1 hour

        //=60 minutes | 1 minute = 60 seconds

        //7 seconds = 1 birth | 13 seconds = 1 death |

   //45 seconds = 1 immigrant

        //365days * 24hours * 60minutes * 60seconds =  

        //31536000 seconds

        double numberOfSecondsInYear = 31536000;

        //After 1 year, number of births (7 seconds = 1

        //birth | plus)

        System.out.println("Current population is

                              312032486");

        //BirthsPerYear is calculated

        double birthsPerYear = numberOfSecondsInYear/7;

        //Display BirthsPerYear

        System.out.println("BrithsPerYear:"

                                       +birthsPerYear);

        //After 1 year, number of deaths (13 seconds = 1

        //death | minus)

        double deathsPerYear = numberOfSecondsInYear / 13;

        //Display DeathsPerYear

        System.out.println("DeathsPerYear:"

                                      +deathsPerYear);

        //After 1 year, number of immigrants (45 seconds =  

          1 immigrant | plus)

        double immigrantsPerYear=numberOfSecondsInYear/45;

        //Display ImmigrantsPerYear

        System.out.println("ImmigrantsPerYear:"

                                   + immigrantsPerYear);

        //Rate per year

        double ratePerYear = birthsPerYear - deathsPerYear

                             + immigrantsPerYear;

        //Display the Result

        System.out.println("RatePerYear: " + ratePerYear);

        System.out.println("End of year 1 the population

                   is"+(int)(intPop + (1 * ratePerYear)));

        System.out.println("End of year 2 the population

                   is"+(int)(intPop + (2 * ratePerYear)));

        System.out.println("End of year 3 the population

                   is"+(int)(intPop + (3 * ratePerYear)));

   System.out.println("End of year 4 the population

               is"+(int)(intPop + (4 * ratePerYear)));

        System.out.println("End of year 5 the population

is"+(int)(intPop + (5 * ratePerYear)));

    }//End of the main

}//End of the class

Output: 

Current population is 312032486

BrithsPerYear: 4505142.857142857

DeathsPerYear: 2425846.153846154

ImmigrantsPerYear: 700800.0

RatePerYear: 2780096.7032967033

End of year 1 the population is 314812582

End of year 2 the population is 317592679

End of year 3 the population is 320372776

End of year 4 the population is 323152872

End of year 5 the population is 325932969
_____________________________________________________________
2.(Algebra solve2*2 linear equation) you can use Cramer's rule to solve the following linear equation:
ax+by=e, cx+dy=f;
x=ed-bf/ad-bc; y=af-ed/ad-bc;
write a program that solves the following equation and display the value for x and y:
 3.4x+ 50.2y= 44.5
2.1x+.55y=5.9

Program Code: 
//CramersRule.java 
import java.util.Scanner; 
public class CramersRule
{
 //Main method 
 public static void main(String[] args)

    {                                            

        // declare variables

        double a, b, c, d, e, f, n1, n2, denominator, x, y;       

        // create Scanner to read user input

        Scanner sc = new Scanner(System.in);

        //Display the values of x,y

        System.out.print("The program solve 2x2 linear

              equation."+"\n The following equation and

              display the value for x and y: 3.4x+50.2y

              =5.9"+"\n 2.1x+.55y=5.9"+"\n a,b,c,d,e,f =  

3.4,50.2,2.1,.55,44.5,5.9");

        // prompt user to enter details

        System.out.print("\n\nEnter a, b, c, d, e, f: ");

        //Read the numbers a,b,c,d,e,f of double datatype

        a = sc.nextDouble();

        b = sc.nextDouble();

        c = sc.nextDouble();

        d = sc.nextDouble();

        e = sc.nextDouble();

        f = sc.nextDouble();      

        //Assign the values of n1,n2 and denominator      

   n1 = ((e * d) - (b * f));

        n2 = ((a * f) - (e * c));

        denominator = ((a * d) - (b * c));

        //calculate x and y

        x = n1 / denominator;

        y = n2 / denominator;

        //Check the statement

        if (denominator == 0)

   {

   //Display the equation has no sol

   System.out.println("\nThe equation has no sol");

        }

   else

  {

  //Display the values of X and y

            System.out.println("x is "+ x +"and y is "+y);

            }//End of the statement

    }//End of the main

}//End of the class

Output: 
This program solves 2x2 linear equations.
The following equation and display the value for x and y:
3.4x + 50.2y = 44.5
2.1x + .55y = 5.9
a, b, c, d, e, f = 3.4, 50.2, 2.1, .55, 44.5, 5.9
Enter a, b, c, d, e, f: 3.4 50.2 2.1 .55 44.5 5.9 
x is 2.623901496861419 and y is 0.7087397392563978