Here is the list of majors at Washington. It shows which majors are competitive.
Business Administration is competitive. These links will provide additional information about admission to the major.
http://foster.uw.edu/academics/degree-programs/undergraduate-programs/admissions/
http://www.washington.edu/students/gencat/academic/school_business.html#UNDER
Your ACT is great and probably would give you a shot at direct admission to Foster, but bear in mind that the average unweighted GPA of this year’s entering class at UW was closer to 3.8. Your upward trend in GPA should help your cause. If you get in but are not among the few who are directly admitted to Foster, your ACT indicates that you have the ability to gain regular admission after completing the prerequisites, provided you apply yourself to your studies.
Good luck!