The following recurrence relation is called the Logistic Equation:

y(k) = y(k-1) + gain * y(k-1) * (1.0 - y(k-1))

This is the equation used to simulate growth in the optional problem-solving. This exercise asks you to use recursion to evaluate successive values generated by the Logistic equation. To get you started, here is a main method that drives recursions for different values of the gain parameter:

Provide a Logistic class that includes the above main method plus a static method named logistic that starts like this:

The logistic method should be tail recursive and include the following terminal conditions:

After getting your program to work, run it with different inputs, and use what you find to describe how y(k) converges for different ranges of gain.

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public static void main(String[] args) { Scanner stdIn = new Scanner (System.in); // Avoid perfectly periodic solution at gain for (double gain-0.05; gain <3.5; gain+ 0.1) ( System.out.println("gain = " + gain); logistic(gain, 0.01, 3.0); System.out.println(); } // end for gain } // end main 2.0