Questions: At the beginning of the semester, procrastinators reported an average of 0.8 symptoms, increasing at a rate of 0.45 symptoms per week. Choose the function that models the average number of symptoms, y, after x weeks.

Solution Steps

To model the average number of symptoms, we need to create a linear function where the initial number of symptoms is 0.8 and the rate of increase is 0.45 symptoms per week. The function will be in the form of $y = mx + b$, where $m$ is the rate of increase and $b$ is the initial number of symptoms.

The average number of symptoms $y$ after $x$ weeks can be modeled by the linear function: $$y = 0.45x + 0.8$$ where $0.45$ is the rate of increase in symptoms per week and $0.8$ is the initial number of symptoms.

To find the average number of symptoms after $x = 5$ weeks, we substitute $x$ into the function: $$y = 0.45(5) + 0.8$$ Calculating this gives: $$y = 2.25 + 0.8 = 3.05$$

Final Answer