Step 1 :The question is asking for a function that models the average number of symptoms, y, after x weeks. Given that the average number of symptoms at the beginning of the semester is 0.8 and it increases at a rate of 0.45 symptoms per week, we can model this as a linear function.
Step 2 :The initial number of symptoms (0.8) is the y-intercept and the rate of increase (0.45) is the slope of the function. Therefore, the function should be in the form of y = mx + b, where m is the slope and b is the y-intercept.
Step 3 :In this case, m = 0.45 and b = 0.8. So, the function should be y = 0.45x + 0.8.
Step 4 :Final Answer: The function that models the average number of symptoms, y, after x weeks is \(\boxed{y = 0.45x + 0.8}\).