I'll look into that and see if my understanding of the function is correct. Thanks again for all your help. Im' about 100x closer to get this working than I was before.

Absolutely

Ok, I was finally able to take a look at this again and I was able to figure it out.

package com.turretgame.mainpackage;

import java.util.List;

import android.graphics.Color;
import android.graphics.Matrix;
import android.util.Log;

import com.example.gamedevchapter3.Input.TouchEvent;
import com.example.gamedevchapter3.Pixmap;
import com.example.gamedevchapter3.Graphics;

public class Turret {

	Pixmap turretImage;
	Matrix matrix;
	
	final int SHIP_X_POS = 360;
	final int SHIP_Y_POS = 1040;
	
	final int SHIP_X_ROTATEPOS = 360 + 15;
	final int SHIP_Y_ROTATEPOS = 1040 + 20;

	final int TOUCH_X_TRANSLATION = 360;
	final int TOUCH_Y_TRANSLATION = 1040;
	
	float direction, tempDirection = 0;
	int xpos, ypos = 100;
	float eventSlope = 0;
	int screenWidth, screenHeight;
	
	float shipPosition[] = {5.0f, 7.0f};
	float shipRotation[] = {0.0f, 0.0f, 0.0f, 1.0f};
	
	float touchPosition[] = {0.0f, -5.0f, 0.0f};
	
	float blendedRotation  = 0.0f;
	float startRotation    = 0.0f;
	float targetRotation   = 180.0f;
	float sliderTime       = 0.0f;
	float incrementTime    = 0.0f;
	 
	float distanceBetweenModels[] = {0.0f, 0.0f, 0.0f};
	
	TouchEvent event;

	public Turret(Pixmap image, int x, int y, int worldWidth, int worldHeight) {
		turretImage = image;
 
		matrix = new Matrix();

		xpos = 360; 
		ypos = 1040;
		matrix.postTranslate(360, 1040);
	}

	public void update(List <TouchEvent> events, float deltaTime) {
		
		for (int i = 0; i < events.size(); i++){
			
			event = events.get(i);
			
		//Log.d("Touch Event Coords", "X value: " + Float.toString(event.x) + "\t Y value: " + Float.toString(event.y));
		
		matrix.reset();	
		matrix.postTranslate(SHIP_X_POS, SHIP_Y_POS);
		
               ////////////////////////////////////////////////////////////
               //this line used to be event.y + SHIP_Y_POS
	       touchPosition[1] = SHIP_Y_POS - event.y;
	       touchPosition[0] = event.x - TOUCH_X_TRANSLATION;
	       /////////////////////////////////////////////////////////////	
		
		//============================= - The next seven lines of code seems to have round 1 taken care of.
	       incrementTime += 0.001;     
	       //--------------------------------    
	       
	       
	       
	       
	       distanceBetweenModels[1] = touchPosition[1]  + shipPosition[1];                                      
	       distanceBetweenModels[0] = touchPosition[0] - shipPosition[0];                                                                  
	 
	       //------------------------------------------------------------------------------------------------------
	 
	       targetRotation = (float) ((float)Math.atan2(distanceBetweenModels[0], distanceBetweenModels[1])* 180 / Math.PI);                    
	 
	       
	       blendedRotation = (float) ((startRotation * (1.0 - sliderTime)) + (targetRotation * sliderTime));                                   
	 
	       matrix.postRotate(blendedRotation, SHIP_X_ROTATEPOS, SHIP_Y_ROTATEPOS);
	       
	       if(sliderTime <= 1.0) // This will prevent the rotation from over-shooting
	       {
	             sliderTime += incrementTime;                                                                                                   
	       }
		}
	}

	public void draw(Graphics g) {

		g.drawPixmap(turretImage, matrix);
		//g.drawLine((int)SHIP_X_ROTATEPOS, (int)SHIP_Y_ROTATEPOS, (int)touchPosition[0] + TOUCH_X_TRANSLATION, (int)touchPosition[1], Color.WHITE);
		g.drawPixel(250, 250, Color.WHITE);
	}
}

The math I was using to translate the touchEvent was backwards. Once I got the coordinates on some graph paper I was able to see it.