Recursion - HalfLife Calculation

[atticus89]

I am working on a recursion function that determines the amount of radioactive material that remains after a given number of years. The decay rate is 1/2 or 50% each year.

I am having a trouble trying to get the recursion setup.

i just cannot seem to get the recursive case right implementing the formula.

The correct result that should finally be returned is 31.25.

    int halflife(int, int);

    int main()
    {
     cout << "The amount of 500 lbs of material after 5 years is " 
     		<< halflife(500, 5) << endl;
    }


    int halflife(int initial, int year)
    {
      if (year == 0)
      return 1;
      else
      return  (halflife(initial, year - 1) * .5);
    }

right now the issue is it is returning 0.03125. which as you can see i very close if i just multiply the result by 1000 however i cannot do that. Any help will be nice

[fprefect]

Please clarify. Are you saying the radioactive level measures 500 at the beginning and the level will decrease by 50% each time interval and you have 5 time intervals?

If yes then your decay should look like:

5=500 then 4=250 then 3=125 then 2=62.5 then 1=31.25 then 0=15.6

So I am not sure where you get the value 0.488281

[atticus89]

The radioactive level measures 500 at the beginning and decrease by 50% or 1/2 each interval.

So the Radioactive Material starting is 500
the decay is 50% or 1/2
the total amount of time of decay is 5 years

What should return is 31.25

Your interval above is going 6 times and not 5.

[atticus89]

edited

[SakurasouBusters]

What do you mean by "HalfLife"?
Is it the famous "Half Life" game you are talking about?

[integralfx]

int halflife(int initial, int year)
Integer division truncates the fractional part.

What should return is 31.25

Your interval above is going 6 times and not 5.

https://puu.sh/rJgqt/d7aef44b70.png

if (year == 0)
      return 1;

How do you know that after n years, there will be exactly 1lb left?

double halflife( int initial, int year )
{
    if( year == 0 ) return 1;
    else {
        double amount{ halflife( initial, year - 1 ) * .5 };
        std::cout << "year = " << year << "\tamount = " << amount << "\n";
        return amount;
    }
}

year = 1	amount = 0.5
year = 2	amount = 0.25
year = 3	amount = 0.125
year = 4	amount = 0.0625
year = 5	amount = 0.03125
The amount of 500 lbs of material after 5 years is 0.03125

right now the issue is it is returning 0.03125. which as you can see i very close if i just multiply the result by 1000 however i cannot do that.

That is just a coincidence.

int main( )
{
    const int initial{ 600 }, time{ 5 };
    
     std::cout << "The amount of " << initial << " lbs of material after " << time << " years is " << halflife( initial, time ) << "\n";
}

year = 1	amount = 0.5
year = 2	amount = 0.25
year = 3	amount = 0.125
year = 4	amount = 0.0625
year = 5	amount = 0.03125
The amount of 600 lbs of material after 5 years is 0.03125

[atticus89]

So now I am completely lost if the calculation is just a coincidence.

Basically I need it to take the recursive function to take a value and cut it in half each time it iterates. using the Year as the counter.

I know that the correct answer if the initial value = 1000 decaying 50% or 1/2 per year for 5 years is 31.25.

just cannot seem to get the function to work as it should...any help please would be appreciated

[integralfx]

You can either do it like this:

double halflife( int initial, int year )
{
    if( year == 0 ) return initial;
    else {
        double amount{ halflife( initial, year - 1 ) * .5 };
        std::cout << "year = " << year << "\tamount = " << amount << "\n";
        return amount;
    }
}

year = 1	amount = 250
year = 2	amount = 125
year = 3	amount = 62.5
year = 4	amount = 31.25
year = 5	amount = 15.625
The amount of 500 lbs of material after 5 years is 15.625

or

double halflife( double initial, int year )
{
    std::cout << "year = " << year << "\tamount = " << initial << "\n";
    
    if( year == 0 ) return initial;
    else return halflife( initial * 0.5, year - 1 );
}

year = 5	amount = 500
year = 4	amount = 250
year = 3	amount = 125
year = 2	amount = 62.5
year = 1	amount = 31.25
year = 0	amount = 15.625
The amount of 500 lbs of material after 5 years is 15.625

With recursive functions, it's extremely helpful to output the values of the parameters, so you can see how the computer unfolds the recursion.

[atticus89]

Thanks, I was able to see that my multiplication of the 1/2 was in the wrong spot and I was returning the wrong value in my base case which is why my return was not coming up incorrectly.