Step 1 :Given the regression equation y = ax + b, where a is the slope of the regression line, b is the y-intercept, x is the number of hours studied per week, and y is the predicted final exam score.
Step 2 :Substitute the given values into the equation: a = 5.64, b = 36.53, and x = 1.
Step 3 :Calculate y = 5.64*1 + 36.53 = 42.17.
Step 4 :Round the predicted score to a whole number: 42.
Step 5 :\(\boxed{42}\) is the predicted final exam score of a student who studies 1 hour per week.