NSolver.java

public class NSolver {

    public static void main(String[] args) {

        /* define total number of iterations (or epsilon) and initial value */
        int iter = 2;
        double epsilon = .00001;

        double t_0 = 0.2;
        int iterCounter = 1;

        /*
         * if choosing to terminate with epsilon then replace the
         * while loop cond w/ iterCounter <= iter, Math.abs(I(t_0)) > epsilon
         */
        while (iterCounter <= iter) {

            t_0 = t_0 - I(t_0) / I1(t_0);

            /* output current data to console */
            System.out.print("Iteration# " + iterCounter);
            System.out.print(", Current (t): " + t_0);
            System.out.println(", Current I(t): " + I(t_0));

            /*
             * check if absolute value of function is within epsilon.
             * if root is found this will break out of loop.
             * this only applies if using epsilon terminating condition.
             */
            if (Math.abs(I(t_0)) <= epsilon)
                break;

            iterCounter++;
        }

        /* output final data to console */
        if (Math.abs(I(t_0)) <= epsilon)
            System.out.println("The root I(t)=0 is at t = " + t_0);
        else
            System.out.println("\nAfter " + (iterCounter-1) + " iterations, " +
                            "the final approximation of the root " +
                            "is t = " + t_0 + ", where I(t) = " + I(t_0));
    }

    /*
     * Define your I(t) in the body of this method.
     * I(t)=1000[1-(1+t)^-30]-135000t
     */
    public static double I(double t) {
        return (1000) * Math.pow(1 - (1 + t), -30) - 135000 * t;
    }

    /*
     * Define your I'(t) in the body of this method.
     * I'(t)=[30000/(t+1)^31] - 135000
     */
    public static double I1(double t) {
        return (30000 * Math.pow(t + 1, -31)) - 135000;
    }
}