Preheat oven to 350F. Spray 8x4 inch loaf pan with nonstick spray. In large bowl, combine flour, baking powder, baking soda and salt. In a small bowl, combine sugar, carrots, applesauce, egg and oil.
Stir apple sauce mixture into flour mixture just until moistened. (batter will be thick) Fold in apricots. Spread batter into prepared pan.
Bake 45 to 50 minutes or until center of loaf test done. Cool in pan 10 minutes. Invert onto wire rack; turn right side up. Cool completely. For best flavor, wrap loaf in plastic wrap or foil; store at room temperature overnight.
Just before serving, in small bowl, combine powdered sugar and apple juice until smooth. Drizzle over top of loaf. Cut into 12 slices.